Dire Avengers: Good long-range firepower, good for killing lots of lightly-armoured foes, they even have a good chance against Marines, their weakness, though, is close combat.
Swooping Hawks: Good flanking and harassment troops, great movement, they shoot fairly well but have lasguns, grenade attacks can take out
artillery and characters, their weakness is no HtH, light armour, and vulnerability to overwatch fire.
Striking Scorpions: Good HtH troops, good armour, but no ranged attack, think of them as Assault troops.
Howling Banshees: Great HtH troops, good armour, and the Banshee's scream, but no ranged attack, strictly Assault troops.
Warp Spiders: Great armour, powerful weapon but short ranged template weapon only, great for killing average or low Initiative troops, not so good against high Initiative troops, Warp Jump gives great movement range.
Dark Reapers: Good armour, some of the best support troops in the game, missile launcher is very versatile, but no HtH weapons except laspistol, -1 in HtH due to heavy weapon.
Fire Dragons: Tank and Character killers, only drawback - only 12" range on the meltagun, and again, weak in HtH is their weakness.
Shining Spears: Great flanking troops, two sustained fire dice, plus laser lance, and speed for the Jetbikes, drawback - exspensive.
Guardians: Don't forget these, very versatile troops.
Eldar Scouts: Good infiltration troops for harassment, but weak on the attack.
Wraithguard: Deadly to everything, fairly good survivability, but very short ranged weapon.
Exodites and Pirates: Give you good additional troops at a cheap point cost.
Weapons Platforms: Best support weapons in the game.
Eldar Dreadnought: I like it, some people don't, I think it is very versatile, and I ususally use one.
War Walker: With the Crystal Targeting Matrix, it is a very good weapon, even without the CTM it is useful to lay down lots of firepower.
Vyper: DEADLY, FAST, LOTS of sustained fire dice, and good armour penetration.
Jetbikes: Fast, great flanking troops, and reasonable point cost.
Harlequins: What can I say? The Harlies do it ALL. Close combat, ranged attack, and great defensively, and awesome characters.
If you will look over this list, you will see that most troops are specialized, and you must coordinate your attack for each troop with its speciality to cover the weaknesses of each of the others while still taking advantage of its own strengths, this can be rather hard to do, but when you get it right, there is very little that can stand before an Eldar army.
In the following tactics, I will try to state them in such a way as to allow for the fact that different players will have different makeups for their armies, so I will give examples and many times I will give an option of troop types to use.
High Ground
This is an objective that will really try the abilities of an Eldar commander, as you must place a heavy weapon on the high ground to get the objective points.
Try to make your setup where you can have platforms and/or Dreads put concentrations of fire on the enemy troops that threaten your high ground objectives. Use mobile and highly armored aspects to take the high ground, then move up your heavy weapon that you intend to occupy it, along with a unit to guard it, Avengers make good units for this. Use Scouts between your objective and your opponent to slow him down and to draw his fire away from your objective, and the heavy weapon occupying it. Other than this, the battle comes down to keeping the high ground and minimizing your losses while maximizing your opponent's losses. Set up lines of fire where you have good cover and can concentrate fire on you opponent's units where it will damage him the most and gain the most victory points for you, it is always best to concentrate your fire. Use your best units to concentrate on eliminating the opponent's best and most
expensive troops. Use your weaker units to hold positions that give them cover and the
opportunity to slow down the enemy units and give covering fire to your attack units.
Dawn Raid
This is one of the better objectives for the Eldar, use the bulk of your army to tie down the enemy while doing as much damage as you can to him. Take a fast moving squad (jetbikes, Swooping Hawks, etc.), keep them behind cover within movement range of your opponent's deployment zone, and just sweep in with them around a flank on the last turn of the game, that will give you your victory points for your objective. I know this is a sneaky tactic, but if you'll read the Dawn Raid card, you will see you are supposed to be sneaky.
Take and Hold
Create a special group of squads in your deployment to take your objective and hold it (I like the following three squads used together: Scouts for screens, Dire Avengers for firepower and to actually hold the objective (or if it's open ground a Dread), and a good strong Aspect squad for counterattacking any opponent that tries to take the objective away from you). Other than this, deploy in such a way as to support your units taking the objective while damaging the opponent while minimizing your own losses. Use your fast troops (jetbikes, Swooping Hawks, etc.) to harass your opponent's flanks and rear areas. If you can take out his psyker, so much the better.
Guerrilla War
For Guerrilla War, deploy in such a way that you will be able to get your best hand to hand troops into combat, preferably with your opponent's troops that will be easy targets for them. Use the bulk of your army to cover your HtH troops and inflict casualties on the enemy for standard victory points, while minimizing your own losses by using cover to your best advantage.
The Assassins
This is another good one for the Eldar. Use psykers and/or Exarchs to kill your opponent's commander. You *must* keep your opponent from knowing that this is your mission until it is too late for him to counter it. Use a diversion, make a feigned attack as if you had one of the other missions like Take and Hold or High Ground. Often this will leave his commander vulnerable. If at all possible, use your psychic powers to strengthen your attack and weaken your opponent's commander (Doom and Guide, Fortune on your own troops is also good for this mission).
Witch Hunt
Most of what I said for The Assassins goes here also, just your target is your opponent's most powerful psyker.
Hold the Line
For Hold the Line, set up in your bunkers and other cover in such a way that your distance weapon troops can lay down crossfires and create a killing zone. Use troops such as your Banshees and Scorpions as reserves to counterattack any enemy that gets into your half of the table and that your distance troops can not cut down. Use Scouts in skirmish line to slow down the enemy and to keep him from firing on your more important troops. Use fast squads (jetbikes, Swooping Hawks, etc.) to harass your enemy's flanks and rear area, and protect your own.
Bunker Assualt
This is not one of my favorite objectives for Eldar. Set up in such a way that you can concentrate heavy weapons fire on the bunkers while giving your troops the best cover you can to minimize their own losses. The only real troops for getting in close and attacking bunkers the Eldar have are Fire Dragons Wraithguard, and Warp Spiders, as their weapons have the best chance of either destroying the bunker, or the garrison inside it, but only do this if you can attack from an angle that is in the bunker's blind spot. Heavy Weapons are still your best choice for destroying the bunkers, so concentrate on them with your heavy weapons, and fight your opponent's other troops with your squads. Always use cover to protect you from the heavy weapons your opponent is sure to set up in his bunkers. Jetbikes with shuriken cannons and Vypers with heavy weapons such as lascannon and heavy plasma are good for bunker busting, but do it from the flanks and/or rear, don't make head-on attacks, and your opponent, if he's any good at all, will be waiting for pop-ups, and have troops and heavy weapons on overwatch, so use cover and flanking attacks instead.
I know that these are very generalized tactics, but without knowing the exact makeup of both armies involved, and the layout of the terrain, they must be. Also, I tried to avoid giving advice to use psykers or special characters because I do not know what restrictions will be placed on your games.