Update Log:
forgot summoner spells @-@
build made.

This is my first guide, please be nice & comment when you vote. This is just how I play Caitlyn.

Pros:
Amazing Range
Easy escape <If you can use your net correctly.>
Similar "ward" skill
Easy to kite with
Passive hits like a truck early game.
Amazing farmer.
Ult's a HUGE snipe.

Cons:
Extremely squishy
Easy taken out with CC
Most likely targeted during team fights
<If anymore I can think of i'll add.>

I chose ArPen red runes because it's a must on ranged attack damage DPS. I got yellow seals because its a MRegen that gradually increases late game. Blue seals for CD reduction to spam your skills easier, and HP or ArPen to either increase survivability early game or be able to pierce more armor.

I chose a 21/0/9 taking more armor pen, improved ghost & improved exp gain.

I chose Flash & Ghost because it makes you harder to hit and be targeted with CC, making you like a true sniper who does not get hit.

There's a doran blade there because its a reliable 100 HP, 8 Damage, & 3% life steal. Usually you want to get more then one so you can have even MORE survivability early game and a bit more damage. Rush your berserker greaves so you can begin chasing enemies and escaping easier. Gradually work through to Last Whisper, Blood Thirster, Black Cleaver, Madred Bloodrazor, and if the game has been going long enough Infinity Edge. The alternatives that you can always get are Frozen Mallet (although I've never gotten this because I don't REALLY like it, because if you have crazy range & if your smart how are you going to take much damage?) Youmuu's GB for it's unique effects and active. If you're a troll & want to mess around get a tiamat.

Early Game: Get your doran blade & health pot and choose a lane. (although I do not recommend a 1v2 lane, they will charge you at level 6 which is extremely dangerous. I also do not recommend mid. I think Caitlyn is most effective if she can work with somebody who has CC, not alone IMO.) ALWAYS LAST HIT. When you've gotten enough money go back for another Doran Blade and if you have enough boots. ALWAYS SPAM YOUR Q, it's a main harass & farming skill. Use your W to scout out bushes to see if anyone is in there. After tons of farming you should get your berserker greaves & start aiming for your last whisper.

Mid Game: You should be having some kills (or deaths if you suck) & some towers should be dead or are being worked on. Now you have your last whisper (Which really hurts nearly everyone) and should be near finishing your blood thirster and starting your black cleaver. Remember to stay behind your team and harass with your Q. Always get red buff (but not if someone else DESPERATELY wants it.)

Late Game: You should be a baller right now, taking down tanks extremely quickly (because your madred is done.) and be sniping people to finish them off. Caitlyn is extremely capable of being amazing if her team can support her. Never run out alone, EVER. You will be targeted and die in seconds.

Well, This is my guide to play Caitlyn, now have fun and there'll be updates sooner or later. :D