For skill specific details this is fully covered at the Guild Wars 2 Wiki on the page Racial Skills. The summary from there says:
[Racial Skills] can be equipped on the five last slots of the skill bar,
depending on their type. They may have various effects, such as
condition removing or changing to a bear form, but they are all
projected to be fairly weaker than their counterparts from professions
that are specialized in similar skills. Each race has 6 skills. Racial
skills will be available from the beginning of the PvE campaign
Skills in this portion of the bar are earned in a similar fashion as skills on the left. Experience and quest completion will unlock them. The first skill is usually granted soon after starting the game and is the top skill in each race from the list below.
As of pre-launch, these are the skills. Click on each race for full details on the skill and how it can be used:
Utility
- Pain Inverter
- Radiation Field
- Technobabble
Elite
- Summon 7-Series Golem
- Summon D-Series Golem
- Summon Power Suit
Healing
Utility
- Grasping Vines
- Seed Turret
Elite
- Summon Druid Spirit
- Summon Fern Mastiff
- Take Root
Utility
Elite
- Become the Bear (Has Auxilary Sidebar)
- Become the Raven (Has Auxilary Sidebar)
- Become the Snow Leopard (Has Auxilary Sidebar)
- Become the Wolf (Has Auxilary Sidebar)
Utility
- Battle Roar
- Hidden Pistol
- Shrapnel Mine
Elite
- Artillery Barrage
- Charrzooka (Has Auxilary Sidebar)
- Warband Support
Healing
Utility
- Prayer to Kormir
- Prayer to Lyssa
Elite
- Avatar of Melandru (Has Auxilary Sidebar)
- Hounds of Balthazar
- Reaper of Grenth
Each class has a specific "F" skill, or multiple "F" skills. Some only have a single ability on F1, while others have 3 or 4 going up through F2, F3 and F4. These are unlocked at different levels, depending on the class, and in some cases depending on your current weapon/skill loadout (or pets when it comes to the ranger).
Warrior - F1 only. Burst skills. Dependent on the weapon you're currently equipped with. A bar fills up with "Adrenaline" as you do damage to your opponents, and the more you have stored up, the more powerful the Burst skill becomes.
Elementalist - Attunements. Fire (F1), Water (F2), Air (F3), Earth (F4). These skills offer the Elementalist the ability to determine what their 1-5 skills will be with their current weapon set up, offering the Elementalist up to 20 available skills per weapon set. For this reason, the Elementalist is one of two professions that does not get a weapon swap.
Guardian - Virtues. The guardian has 3 Virtues (F1, F2, F3). These are self only "buffs" that offer unique attributes to the Guardian. When used, they offer their bonus immediately to all allies in the area at the cost of going on cooldown and not offering their passive bonus to the Guardian until they are refreshed.
Necromancer - F1 only. Death Shroud. Puts the Necromancer into a ghastly form, giving them a new bar that counts as their health, as well as a new ability bar. When the health bar in Death Shroud is depleted, the Necromancer merely reverts back to their normal form, rather than dying.
Mesmer - Shatter Illusions. Each of the 4 shatters provides a different effect, and is affected by the number of Illusions / Phantasms currently active. Your shatters can explode for damage, apply stacks of confusion, apply dazes, or provide a unique buff to the Mesmer called "Distortion" which is, essentially, a short invulnerability.
Engineer - Tool Belt. Based on the Engineer's healing (6) slot, as well as utility (7, 8, 9) slots, the Tool Belt is usually a one-off effect of the respective slot. For example, having the Mine Kit equipped in your 6th slot offers a unique mine-based ability on your F2 key. Because the Engineer has such a versatile loadout with utility / healing weapon kits, as well as F keys being influenced by loadout, they are one of the two professions that do not have a weapon swap function.
Ranger - Pet abilities. Each pet has an active ability that is controlled by the F keys, as well as the ability to command your pets and swap pets.
Thief - F1 only. Steal. Thieves can steal from (supposedly) any hostile NPC or hostile PC, providing them with a pseudo-random ability in return. This ability that they gain is a 1 time use.
Best Answer
The main strategy for this is three-pronged. First, look at your traits: one or both of the attributes associated with the trait line that contains traits improving that weapon will usually be the attribute(s) that benefits that weapon the most.
Next look at the skills the weapon provides, especially the auto-attack. If it inflicts conditions, you probably want condition damage and some condition duration. If it attacks quickly, you may want a lot of precision, to try to rack up a lot of bonuses from crits. If it heals you somehow (necromancer dagger, guardian mace, elementalist water daggers) you may want healing power. If its attacks are slower and don't have any particular other attribute benefiting them, you probably want power. Usually you should be ending up with one (or both) of the two attributes you identified in the first stage; if it's not, proceed carefully, as this may mean you're not imagining playing that weapon the way ArenaNet designed it to play.
Finally, if you still have attributes you can be boosting, take a look at the attributes that synergize well or would cover some of your weaknesses. If you're boosting condition damage, condition duration tends to work well. If you're boosting precision, a little extra crit damage % goes a long way. If you're pumping power, a little precision can help noticeably. Alternately, cover your weak areas. If you're heavily invested in an offensive trait line and have pushed a bit into a 2nd offensive line, consider going relatively deep into a defensive trait line to pick up some toughness or vitality. High vitality builds also probably want healing power, so they can actually restore all those hit points.
Lets take scepter for the necromancer as an example. First we look for the traits that improve scepter; we find them in the Curses line, which boosts precision and condition damage. Next we look at the scepter's basic attack and notice a decent attack speed and not one but two damaging conditions inflicted. Condition damage will definitely be our primary damage stat, and since boosting its trait also boosts precision, we'll want to keep an eye out for ways to cause conditions on crits as well as further precision boosts. Finally we consider other attributes; with all those conditions & condition damage, some condition duration would be helpful, and some extra power, which condition duration shares a trait line with, never hurts. We may also want to grab a defensive stat, though, to try to avoid being a glass cannon; if we've got anything with lifesteal in our off-hand it may be worth grabbing vitality & healing, otherwise I tend to gravitate towards toughness.
Here's the build I use on my scepter necro (off-hand warhorn, staff secondary) in sPvP: