I'm not a huge fan of intros, as I think they're boring and a waste of time. So basically, this is a short and sweet guide to Caitlyn, good if you don't feel like reading all day and just want the point (:

Piltover Peacemaker: Caitlyn readies herself for one second, then fires a decently ranged bullet, dealing a nice amount of damage to enemies and/or minions. Subsequent targets receive less damage.
Yordle Snap Trap: Caitlyn sets up to three visible traps at a time. If an enemy steps on one, they are immobilized and take magic damage for 1.5 seconds.
90 Caliber Net: Caitlyn fires a net at a target, slowing them, dealing a little damage, and knocking herself in the opposite direction.
Ace in the Hole: Caitlyn channels for a moment and then snipes her target from a far distance.

Before we get into the abilities, I wanna talk about Cait's passive, her . Every 8 shots, she fires an extra powered shot. However if Cait is shooting from the brush, it reduces to every 4 shots. Therefore, anytime you get a chance, farm/harass from the brush to fire headshot more often. Another point I wanna make is that shoot minions for seven shots, and when headshot is ready, shoot it at an enemy champ + piltover peacemaker for a stronger, more effective harass.

Level up Piltover Peacemaker and the 90 Caliber Net first. Unless you are playing against a sneaky team, in which the traps would be more helpful.

Piltover Peacemaker is Cait's core damage outputter. It's great for harassing enemies because of its long range. Its also great for farming minion waves as its the only ablity of Cait's that hits more than one target at a time. It's a skillshot, so it may take some time to master hitting the enemy.

90 Caliber Net can also be used in a variety of ways. Its a good way to escape from being chased down from enemies, bouncing out of turret zones, and getting out of the middle of a team fight. As for using it as a slow, its not so helpful because it knocks you out of range. If you're up against a wall, then it would work as a slow because you'd hit the wall.

The Yordle Snap Traps are cool except for the fact that they're visible to the enemy team. However, I've found that placing them in bushes is effective since when an enemy steps on one, it reveals who's hiding in the bushes. Also, if you wanna see who's in the bushes, if you throw a trap in there, it reveals them for about a half a second. Honestly, they don't do much other than that for me 90% of the games, so I level them up last.

Ace in the Hole has got to be my favorite ablilty in the entire game. It has extreeeeeeeeemely long range and satisfies the need to kill enemies running away with two or three bars of health left. Obviously, leveling this up whenever possible is recommended.

Doran's blade is a great starting out item for Cait, as the extra 100 health helps her from being torn apart in early game.
However, if you're more of a careful player, Vampiric Scepter and a Health Potion may be a better choice to pick, so that you can build into The Bloodthirster more quickly. The lifesteal helps you gain health lost back from minions, so long as you stay out of harrasing range of the enemy.
I prefer to build into The Bloodthirster first because it has a decent amount of damage and lifesteal, which is great for Cait because she is really squishy. I usually get the Vampiric Scepter because its cheaper and then when I save up enough gold (which should be no problem) I purchase the B.F. Sword then upgrade it to The Bloodthirster.
Infinity Edge's extra damage is amazing, and worth the hefty price.
madred's bloodrazors Madred's Bloodrazor adds damage.
The Black Cleaver adds damage and attack speed.
Last Whisper is a great deal for the price, considering it's high armor penetration percentage.

basnhee's veil Banshee's Veil: If you find that you're not doing so hot, throw in a Banshee's Veil for a bit of protection.

The way I play Caitlyn works for me, however it might not for you. This is in no way guaranteed.

Early Game:
Grab your first item and go mid. HURRY getting there! Before the minions have spawned, go close enough to the enemy's tower (without getting hit) to where it reveals the champion standing there. If there is an enemy standing there by his turret, fire a Piltover Peacemaker their way. This takes a nice chunk of their health. Run away. If the enemy fires back, they will most likely miss and have to wait for the next cooldown, giving you a chance to autoattack. Cait's basic attack is pretty strong so it gets them down even lower. If they still don't run away, sacrifice the health you're taking from their hits for the first blood. Then recall and hurry to catch up with the minions. However if things go sour and you don't think you can kill them first, run or Flash and Ghost away! The key to this is to get there quickly. If not, they could be waiting in the brush for you, so you wanna hurry down there the fastest you can to avoid getting trapped between them and the tower.

After minions have spawned, Cait should focus on farming. Last hitting minions is easy with her, so the gold should be piling up quickly. Remember, you have a longer range than your enemy most likely, so use that to your advantage and harass them out of the way. This will keep them from gaining gold and experience, giving you the upper hand. Never cross the river by yourself, as you will be ganked. Wait for the enemy to push back into a safer zone for you and farm minions again. Repeat this over and over until you get a chance to attack the tower along with your minions, without a chance of being ganked. While attacking the tower, be very weary of the three M's: Minions, MIA's, and the map. Keep an eye on the map to make sure you can see all of the enemies. If one dissapears into the jungle, back away, for they are most likely coming in for a gank. MIAs are convienent, however you can't always rely on them so this is the only way to be sure. Watch the minons. If the tower is hitting the last ally minion, back off otherwise you'll be hit by the tower. (Duh.)

Midgame:
Once you've destroyed the tower, you begin mid game. For me, this is the funnest part of the game. Concentrate on keeping the enemy minion waves away from your tower, being weary of ganks, and ganking. Once you feel that the mid tower is safe for a while, go either top or bottom and depending on the situation, either gank the enemy or help push. Keep an eye on mid lane! If it looks like the enemy is getting the advantage on mid, leave and go back to mid lane to keep them off your tower.

Lategame:
Caitlyn is known for being quite useless end game. I see why people would think this, however I've found it to be not completely true. When pushing as a team, Cait should always stay in the back for two reasons: 1) She has a long range, so she doesnt need to be at the front, and 2) she's targeted first by the other team since she dies easily. Spam piltover peacemaker, and watch for enemies running away with low health that the rest of the team can't catch up to to kill. Ace in the Hole will take care of that. (See the section titled ACE IN THE HOLE for more information.)

Cait's ultimate is great. However it also has it's cons.

It has ahhhmazing range and is awesome for killing those enemies who think theyre smart enough to just run away once you've got them down to low health. Just pop your ult on them and boom--theyre dead.

The negative parts about her ult:
Channeling: Cait has to channel up her ult before firing which is bad for 3 reasons:

1) If you're 1v1 and need a quick burst of damage, it takes too long to charge up, giving the opponent time to kill you.
2) The channeling process can be interrupted, causing you to waste your ultimate and possibly risk your life.
3) Caitlyn cannot move while channeling which makes her vulnerable to being gang raped.

Interception: The bullet can be intercepted by another team member on the opponent's side. For example, say you're aiming at a Viegar with a bar of health left that is running for his life. You aim your ult at him and fire but--ugh--they're tank, Warwick, jumps in front of Viegar and takes the bullet for him, barely knocking his own health down at all.

Therefore, her ult has to be thought out before it's used. Think to yourself: Am I in a safe place to start channeling? Is someone gonna take the bullet and make me waste it? If the answer is no and then yes, think twice before firing.

Caitlyn can't solo a team. So when you have a sucky team, you lose (defeats)

As for the games where I went negative, I made the mistake of not protecting Cait.

Sometimes if you're just getting eaten alive, an item with armor and health would be usefull.

I suggest Banshee's Veil.