The short answer is that you are right. In your turn you may make 1 standard action and a move action, or a full round action, along with one or more free actions - source

A single attack is a standard action, as is using an ability. When used as such you get a single standard action, plus a move. That means you can only use your ability once per round (certain abilities may have limits on number of times per day or length between uses) - source

When using your BAB to get more than one attack, you don't get as many standard actions as you have attacks in your BAB, but take a full round action. This is the same if you get multiple attacks from BAB, or whether it's from a haste spell, or from a double weapon, such as a quarter-staff. Other abilities that specifically say 1 round for time it takes to complete, rather than standard, also use a full round action. - source

TLDR; Your BAB only counts for a full round action, it doesn't give you many standard actions.

Natural Weapons and How to Use Them

I'm going to summarize here. Keep in mind a vast (maybe even overwelming) number of exceptions exist to modify this very basic summary. This is deliberately the game at its most basic. Natural attacks are detailed here and here and in the Monster Manual under the headings Attack and Full Attack on page 6 and in the entry Natural Weapons on page 312.

Standard Attack

During a standard attack a creature can either...

• attack with 1 weapon (e.g. a longsword, an unarmed strike, a composite longbow), making 1 attack at its full Base Attack Bonus; or...
• attack with 1 unoccupied natural weapon (e.g. a slam, a bite, or a claw that's not wielding a weapon), making 1 attack at its full Base Attack Bonus that inflicts additional damage equal to the creature's Strength modifier. This attack is with the natural weapon in an unarmed creature's Attack entry in the Monster Manual.

Full Attack

During a full attack, which is what a creature gets when using the extraordinary ability pounce (MM 313), a creature can either...

Do This:

• attack with 1 weapon (e.g. a longsword, an unarmed strike, a composite longbow), making 1 attack at its full Base Attack Bonus and a second attack at a -5 penalty if its Base Attack Bonus is +6 or greater, a third attack at a -10 penalty if its Base Attack Bonus is +11 or greater, and a fourth attack at a -15 penalty if its Base Attack Bonus is +16 or greater; and also...
• attack with all its unoccupied natural weapons (e.g. the creature normally has a claw, a claw, and a bite but wields a one-handed weapon, rendering 1 claw unavailable as a natural attack), making 1 attack with each natural weapon at its full Base Attack Bonus with a -5 penalty with each attack inflicting additional damage equal to half the creature's Strength modifier.

Or Do This:

• attack with all its natural weapons (e.g. claw, claw, bite), making 1 attack with each of its primary natural weapons (i.e. the natural weapon listed in the creature's Attack entry, but sometimes a creature has multiple primary natural weapons (e.g. claws) in its Full Attack entry) at its full Base Attack Bonus that inflict additional damage equal to the creature's Strength modifier, and then making 1 attack with each remaining natural weapon at the creature's Base Attack Bonus with a -5 penalty with each attack inflicting additional damage equal to half the creature's Strength modifier.

That -5 penalty to the natural weapons' attack rolls is reduced by the feats Multiattack and Improved Multiattack.

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Example 1

Alvin the human Drd8 uses his supernatural ability wild shape to change his form into that of a lion (MM 274-5). As the ability wild shape is like the supernatural ability alternate form (MM 305), we learn that he loses his human form's natural weapons (of which he had none) but gains the lion's natural weapons and replaces his Str 8 with the lion's Str 21. We're ignoring other adjustment for convenience.

When Alvin in lion form attacks he uses his character's Base Attack Bonus +6 and gains a +5 bonus to attack rolls from his lion form's Strength score. Again, we're ignoring other adjustment for convenience.

Standard Attack

• When Alvin in lion form makes a standard attack with a natural weapon, he uses his claw, making 1 attack at a +11 bonus to his attack roll that inflicts 1d4+5 points of damage.

Full Attack

• When Alvin in lion form makes a full attack and uses only his natural weapons, he attacks once with each claw, each at a +11 bonus to his attack roll, and each inflicting 1d4+5 points of damage. Then he attacks with his bite at a +6 bonus to his attack roll, inflicting 1d8+2 points of damage.

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Example 2

Alvin the human Drd8 uses his supernatural ability wild shape to change his form into that of an ape (MM 268). As the ability wild shape is like the supernatural ability alternate form (MM 305), we learn that he loses his human form's natural weapons (of which he had none) but gains the ape's natural weapons and replaces his Str 8 with the ape's Str 21. We're ignoring other adjustment for convenience.

When Alvin in ape form attacks he uses his character's Base Attack Bonus +6 and gains a +5 bonus to attack rolls from his ape form's Strength score. Again, we're ignoring other adjustment for convenience.

Standard Attacks

• When Alvin in ape form makes a standard attack with a natural weapon, he uses his claw, making 1 attack at a +11 bonus to his attack roll that inflicts 1d6+5 points of damage.
• When Alvin in ape form makes a standard attack with a scimitar, he makes 1 attack at a +11 bonus to his attack roll that inflicts points of 1d6+5 damage.
• When Alvin in ape form makes a standard attack with a spear, he makes 1 attack at a +11 bonus to his attack roll that inflicts 1d8+7 points of damage.

Full Attacks

• When Alvin in ape form makes a full attack and uses only his natural weapons, he attacks once with each claw, each at a +11 bonus to his attack roll, and each inflicting 1d6+5 points of damage. Then he attacks with his bite at a +6 bonus to his attack roll, inflicting 1d6+2 points of damage.
• When Alvin in ape form makes a full attack armed with a scimitar used one-handed, he makes attacks 2 attacks with the scimitar, the first at a +11 bonus to his attack roll and the second at a +6 bonus to his attack roll, but both attacks inflict 1d6+5 points of damage. He can then attack with his remaining natural weapons, making 1 claw attack and 1 bite attack, each with a +6 bonus to his attack roll and each inflicting 1d6+2 points of damage. He can't attack with the other claw because it's full of scimitar.
• When Alvin in ape form makes a full attack armed with a spear, he makes attacks 2 attacks with the spear, the first at a +11 bonus to his attack roll and the second at a +6 bonus to his attack roll, but both attacks inflict 1d8+7 points of damage. He can then attack with his remaining natural weapon, making 1 bite attack with a +6 bonus to his attack roll and inflicting 1d6+2 points of damage. He can't attack with either claw because his claws are full of spear.

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Example 3

Alvin the human Drd18 uses his supernatural ability wild shape to change his form into that of a dire shark (MM 64-5). As the ability wild shape is like the supernatural ability alternate form (MM 305), we learn that he loses his human form's natural weapons (of which he had none) but gains the dire shark's natural weapons and replaces his Str 8 with the dire shark's Str 23. We're ignoring other adjustment for convenience.

When Alvin in dire shark form attacks he uses his character's Base Attack Bonus +13 and gains a +6 bonus to attack rolls from his dire shark form's Strength score. Again, we're ignoring other adjustment for convenience.

After using his wild shape ability Alvin, now in dire shark form, has his followers garb him in Huge nonhumanoid hide armor (PH 123) (120 gp; 125 lbs.) with Huge spiked armor/armor spikes (PH 121, 124) (200 gp; 50 lbs.). To avoid the -4 nonproficiency penalty Alvin has taken the feat Martial Weapon Proficiency (spiked armor/armor spikes) (PH 97).

Standard Attack

• When Alvin in dire shark form makes a standard attack with a natural weapon, he uses his bite, making 1 attack at a +19 bonus to his attack roll that inflicts 2d8+9 points of damage; this damage is 1.5x the dire shark's Strength modifier because the dire shark has only 1 natural attack (MM 6).
• When Alvin in dire shark form makes a standard attack with his spiked armor/armor spikes, he makes 1 attack at a +19 bonus to his attack roll that inflicts 2d6+6 points of damage.

Full Attack

• When Alvin in dire shark form makes a full attack with a natural weapon, he uses his bite, making 1 attack at a +19 bonus to his attack roll that inflicts 2d8+9 points of damage; this damage is 1.5x the dire shark's Strength modifier because the dire shark has only 1 natural attack (MM 6).
• When Alvin in dire shark form makes a full attack with his spiked armor/armor spikes, he makes 3 attacks with the spiked armor/armor spikes, the first attack at a +19 bonus to his attack roll, the second at a +14 to his attack roll, and the third at a +9 to his attack roll, and each attack inflicts 2d6+6 points of damage. He can then also make an attack with his only natural weapon, his bite, at a +14 to his attack roll that inflicts 2d8+3, the -5 penalty and the only-half--Strength-modifier-to-damage because his bite's being used as a secondary natural attack.

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Example 4

Alvin the human Drd18 uses his supernatural ability wild shape to change his form into that of a tendriculos (MM 241-2). As the ability wild shape is like the supernatural ability alternate form (MM 305), we learn that he loses his human form's natural weapons (of which he had none) but gains the tendriculos's natural weapons and replaces his Str 8 with the tendriculos's Str 28. We're ignoring other adjustment for convenience.

When Alvin in tendriculos form attacks he uses his character's Base Attack Bonus +13 and gains a +9 bonus to attack rolls from his tendriculos form's Strength score. Again, we're ignoring other adjustment for convenience.

After using his wild shape ability Alvin, now in tendriculos form, has his followers garb him in Huge nonhumanoid hide armor (PH 123) (120 gp; 125 lbs.) with Huge spiked armor/armor spikes (PH 121, 124) (200 gp; 50 lbs.). To avoid the -4 nonproficiency penalty Alvin has taken the feat Martial Weapon Proficiency (spiked armor/armor spikes) (PH 97).

Standard Attack

• When Alvin in tendriculos form makes a standard attack with a natural weapon, he uses his bite, making 1 attack at a +22 bonus to his attack roll that inflicts 2d8+9 points of damage.
• When Alvin in tendriculos form makes a standard attack with his spiked armor/armor spikes, he makes 1 attack at a +22 bonus to his attack roll that inflicts 2d6+9 points of damage.

Full Attack

• When Alvin in tendriculos form makes a full attack with his natural weapons, he uses his bite, making 1 attack at a +22 bonus to his attack roll that inflicts 2d8+9 points of damage; and his tendrils, making 2 attacks total--one with each tendril--at +17 to each attack roll and each inflicting 1d6+4 points of damage.
• When Alvin in tendriculos form makes a full attack with his spiked armor/armor spikes, he makes 3 attacks with the spiked armor/armor spikes, the first attack at a +22 bonus to his attack roll, the second at a +17 to his attack roll, and the third at a +12 to his attack roll, and each attack inflicts 2d6+9 points of damage. He can then also make an attack with all 3 of his natural weapons--his bite and both tendrils-- each at +17 to his attack roll, with the bite inflicting 2d8+4 points of damage and each tendril inflicting 1d6+4 points of damage, the -5 penalty and the only-half--Strength-modifier-to-damage because all his natural weapons are being used as a secondary natural attacks.

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Example 5

Alvin the human Drd20 uses his supernatural ability wild shape to change his form into that of a 16 HD Huge earth elemental (MM 97-8). As the ability wild shape is like the supernatural ability alternate form (MM 305), we learn that he loses his human form's natural weapons (of which he had none) but gains the 16 HD Huge earth elemental's natural weapons and replaces his Str 8 with the 16 HD Huge earth elemental's Str 29. We're ignoring other adjustment for convenience.

When Alvin in 16 HD Huge earth elemental form attacks he uses his character's Base Attack Bonus +15 and gains a +9 bonus to attack rolls from his 16 HD Huge earth elemental form's Strength score. Again, we're ignoring other adjustment for convenience.

Standard Attack

• When Alvin in 16 HD Huge earth elemental form makes a standard attack with a natural weapon, he uses his slam, making 1 attack at a +24 bonus to his attack roll that inflicts 2d10+9 points of damage.
• When Alvin in 16 HD Huge earth elemental form makes a standard attack with his Huge scimitar wielded one-handed, he makes 1 attack at a +24 bonus to his attack roll that inflicts 2d6+9 points of damage.
• When Alvin in 16 HD Huge earth elemental form makes a standard attack with his Huge spear, he makes 1 attack at a +24 bonus to his attack roll that inflicts 3d6+12 points of damage.

Full Attack

• When Alvin in 16 HD Huge earth elemental form makes a full attack with his natural weapons, he uses two slams, making each attack at a +24 bonus to his attack roll, and having each attack inflict 2d10+9 points of damage.
• When Alvin in 16 HD Huge earth elemental form makes a full attack with his Huge scimitar wielded one-handed, he makes 3 attacks, the first at a +24 bonus to his attack roll, the second at a +19 to his attack roll, and the third at a +14 to his attack roll, and each inflicting 2d6+9 points of damage. Then he makes a slam attack at a +19 bonus to his attack roll that inflicts 2d10+4 points of damage; he can't make a second slam--his second slam is full of scimitar.
• When Alvin in 16 HD Huge earth elemental form makes a full attack with his Huge spear, he makes 3 attacks, the first at a +24 bonus to his attack roll, the second at a +19 to his attack roll, and the third at a +14 to his attack roll, and each inflicting 3d6+12 points of damage. He can't make any slams because both slams are full of spear.

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Using Magic Items While in Wild Shape

The easiest way to use magic items that your new form can also use is, while in your original form, drop the items nearby, use the wild shape ability to assume a new form, and then pick up the items again (or have a friendly creature secure them if the new shape lacks hands or whatever). That's usually not an option if starting combat in one's original form, though. Here are additional magic items that help magic items be functional while using the wild shape ability.

• The slotless item wilding clasp (MIC 190) (4,000 gp; 0 lbs.) attaches to any magic item worn on the body and prevents the worn item from melding, allowing it to function for the new form if the new form could wear the item in a reasonable manner (i.e. a bear could wear a hat of disguise with a wilding clasp attached, but a snake couldn't wear a vest of resistance even with a wilding clasp attached).
• The armor special ability beastskin (MIC 7) (+2 bonus) allows worn armor to transform into armor for the new form when the creature uses the wild shape ability instead of the armor melding into the new form.
• The armor special ability wild (DMG 219) (+3 bonus) makes worn armor or a carried shield meld invisibly with the new form assumed by the wild shape ability, but the armor or shield with the wild ability continues to grant to the creature's Armor Class the armor bonus or shield bonus and the armor's or shield's enhancement bonuses.

That's about it. What you're supposed to do is take the feat Natural Spell (PH 98) and cast spells on yourself while (and, obviously, before) you're in wild shape to compensate for your lack of magic items.