There's no way of finding out all of the information for the covenants in-game. Some things are hinted, others you will find through trial and error. For in-depth information regarding covenants I advice you to check one of the several Dark Souls wikis, such as these: Dark Souls Wikidot, Dark Souls Wikispaces or Dark Souls IGN Wiki Guide.
There are nine covenants in the game.
As a general rule, joining a Covenant and following it's rules provides you with one or several rewards. Sometimes, there's also a penalty for betraying a Covenant (killing a NPC aligned with such Covenant or joining a different one).
Some covenants allow you to rank up your alignment by offering a particular item, in order to get additional rewards.
Here's some info I gathered from my first play-through and some info digging. (This list is not complete):
Way of White
How To Join
- Talk to Petrus of Thorolund in Firelink Shrine
- You can also join by speaking to Rhea of Thorolund after rescuing from the Tomb of Giants. She will be praying inside the church at Undead Parish after her rescue
Rewards
- Grants immediate access to Miracles sold by Petrus of Thorolund:
- Heal
- Great Heal Excerpt
- Homeward
- Force
- Seek Guidance
- Grants higher priority to be matched with online players of these Covenants:
- Way of White
- Warrior of Sunlight
- Princess's Guard
Penalties
Notes
- You can still get Petrus' miracles later on in the game without having to join this covenant
Blade of the Darkmoon
How To Join
- Find the Darkmoon Seance Ring in The Catacombs. If you equip it, a hidden path, located where the second bonfire in Anor Londo lies will be revealed. You will have the option to interact with the carpet before the fog wall and join the covenant
Rewards
- Awards the Blue Eye Orb which allows you to invade the worlds of players who have sinned
- Awards the Blade of the Darkmoon Covenant Ring which, when equipped, summons you to worlds of players who have killed Gwynevere and turned Anor Londo dark
- Awards the Darkmoon Blade Miracle (Rank 1)
- Awards the Darkmoon Talisman (Rank 1)
Notes
- Crossing the fog gate next to the carpet in Anor Londo will prevent you from joining the covenant for the rest of the game
- Killing players as a Blue Phantom awards you with Souvenirs of Reprisal which can be used to rank up this covenant
- Ranking up this covenant beyond Rank 1 (up to Rank 3) strengthens your Darkmoon Blade Miracle
Princess's Guard
How to Join
- After defeating Ornstein and Smough in Anor Londo, you'll have access to the chamber where Gwynevere is. Speak to her to join this covenant
Rewards
- Awards the Ring of the Sun Princess
- Grants higher priority to be matched with online players of these Covenants:
- Way of White
- Warrior of Sunlight
- Princess's Guard
- Grants "permission" to use the following Miracles:
- Soothing Sunlight
- Bountiful Sunlight
Notes
- You can still obtain the Soothing and Bountiful Sunlight miracles for the trophy, you just can't use them without being a member of the covenant
Path of the Dragon
How To Join
- Talk to the Everlasting Dragon in Ash Lake
Rewards
- Awards the Everlasting Dragon Eye which allows you to challenge other players online to earn Dragon Scales
- Awards the Dragon Head Stone
- Boosts your Estus Flask x10 without any bonfire kindling required
- Awards the Dragon Torso Stone (Rank 2)
Notes
- You can trade in Dragon Scales to rank up this covenant
- The use of Dragon Stone and Dragon Torso allows you to transform into a dragonoid. In this form you can cast a flame spell
- Ranking up this covenant strengthens your dragonoid flame spell
Forest Hunter
How to Join
- Speak with Alvina, the cat in Darkroot Garden. Answer YES to all of her questions
Rewards
- Awards the Cat Covenant Ring
- Spawns the vendor Shiva of the East
- Awards Divine Blessing consumable (Rank 1)
- Awards the Ring of Fog (Rank 2)
Notes
- When equipping the Cat Covenant Ring, you may be summoned to protect the forest from other players online
- Ranking up this covenant is achieved by slaying intruders. One kill for Rank 1 and three kills for Rank 2
Warrior of Sunlight
How To Join
- Level up your Faith to 25 and head to the bonfire beneath the Red Drake in Undead Parish. Next to it you will find an altar you can pray at, allowing you to join the covenant
Rewards
- Awards the Lightning Spear Miracle
Awards the Praise the Sun Gesture (You can obtain it without joining)
- Grants higher priority to be matched with online players of these Covenants:
- Way of White
- Warrior of Sunlight
- Princess's Guard
Penalties
- Takes the Lightning Spear Miracle away from you
Notes
- You can substantially lower the Faith requirement by helping online players defeat area bosses. Each boss kill lowers the requirement by 5 points. To be summoned to other worlds, place a summoning sign using the White Soapstone obtained from Knight Solaire
Darkwraith
How To Join
- Talk to Darkstalker Kaathe in the Abyss. To get to the Abyss you will need the key to the seal in New Londo Ruins from Ingward, an NPC in the same area. Also, if you have obtained the Lordvessel, it's mandatory that you do not speak to Frampt (which prompts you to place the Lordvessel on the Firelink Altar).
- You will also have to kill the Four Kings before being able to speak to Kaathe.
Rewards
- Grants you the Dark Hand (Shield/Weapon that allows the absorption of Humanity)
- Grants you the option to buy the Cracked Red Eye Orb (Rank 1)
- Grants you the Dark Armor Set and Dark Sword (Rank 2)
Notes
- Ranking up this covenant is achieved by turning in Humanity.
Gravelord Servant
How To Join
- To join, you have to talk to Gravelord Nito who lies inside an area in The Catacombs, only reachable via an empty coffin, next to a Titanite Demon. Of course, this must be done before you kill Gravelord Nito as part of the story progression.
Rewards
- Awards the Gravelord Sword
- Awards the Gravelord Sword Dance Miracle
- Awards the Gravelord Great Sword Dance Miracle (Rank 1)
- Grants you the ability to earn Souls and Eye of Death for killing cursed players
Notes
- In order to rank up this covenant, you must turn in Eyes of Death dropped by Basilisks or obtained through PVP.
Chaos Servant
How To Join
- Speak with Queelag's Sister in order to join. She lays pass a secret door, on the lower portion of the tower where you ring the second bell, after killing Queelag.
Rewards
- Awards the Great Chaos Fireball Pyromancy
- Awards the Chaos Storm Pyromancy (Rank 2)
- Opens up a shortcut from Demon Ruins to Lost Izalith (Rank 2)
Notes
- Ranking up this covenant is achieved by turning in Humanity.
There is an NPC, Kingseeker Frampt, that will consume your items in exchange for souls. He appears near the Firelink Shrine after you have rung the two bells. So yes, there is a way to sell item, but not until later in the game.
However, there is almost no limit to the number of items you can have in your inventory (see this question Is there a limit to the number of item in inventory?). You can hold up to 1984 different items in your inventory, and if you purchase the Bottomless Box, from a merchant in the Depth, you can store all those items in it and have a manageable inventory.
However, I think you should just drop the duplicate items because the resell value is really low. This table, from one of the Dark Souls wiki, shows how many souls you'll gain from each class of item:
Weapons 50
Armor 100
Dung Pie 200
Cracked Red Eye Orb 500
Copper Coin 1000
Some unique items 5000
Even if you resell 1000 longswords, you'll only gain 50000 souls. Compared to the time it will take you to sell all of them, and to manage your inventory, I think it is not a good trade-off. There are quicker ways farm souls.
During your second play through, reselling some of the unique items may be a cheap way to get some souls. However, reselling basic items does not seem interesting to me.
Best Answer
If I am thinking of the same giant you are referring to, this is how to get to him...
Starting from the beginning of the fortress, after you get past the gate entrance with the two lizards, you enter the start of the guillotine area, drop down to the left and enter the little entrance way shown in the picture.
Climb the ladder in there to the top and there should be a secret entrance behind an arch. Get through that, climb the ladder behind it and it takes you straight to him.
Here are some pictures to point things out, the pictures follow the order of events I described. So it should be self explanatory to get to the giant, hope it helps out.