Hello my summoners name is DaMechato, and I like to play caitlyn.
I made this build pure of what I though is best. You don't have to obay this build, but you can try it.

Caitlyn is a great AD carry, in my opinion one of the best. She is strong early game and stronger late game (If played well :P ).

Here will be my guide on how to play her.

I chose alot of ad runes to do a lot of damage in early game, this will make her also stronger late game.
I also chose armor because mostly all ADC go bot, so you have defence against their ADC. If you dont have enough armor they can deal more damage.

I chose these masteries because this is a perfect ADC mastery in my opinion.
Although there might be a better one, I like this one the best.
Its got great offence and also a bit of defence.

I chose The Bloodthirster before Infinity edge because, it has to charge up, and you will charge up with minion kills, and with those you can still buy other items. After The Bloodthirster I chose Phantom Dancer because if I have alot of lifesteal AND attack speed, I can heal rapidly. Then I chose Infinity Edge because also having alot of AD and crit chance with the Att.spd. is really working out for me. Next i chose Guardian Angel because if you still die youll have a 2nd chance to steal their life and kill them. Then I chose The Bloodthirster again to steal even MORE health! It would be harder to kill you if you constantly shoot with your basic attacks and heal!

I chose the W skill first, because you can put the trap in the bush to check if someone is there, or when they go there! You can also put a trap in the bush in the river so you wont be ganked so easily. Then I chose then Q skill because everyone needs some agression, and you can poke the enemy HARDCORE. You can also later shoot this at minions to kill them instantly(Yes later you can also kill them with your basic attack but your Q skill is better!). Afterwards I chose E. Now most people would want to lvl Q at lvl 3 again BUT with your E you can chase enemies or escape them!. I lvl the Q skill first to its max before any other skill gets to its max because im a quite offencive player. Then my W because it is really helpful and it can get you kills (How you ask? When they walk into a bush that you have a trap in, they will stop for a while get a little bit damage but you arrive there and you can kill them!)

I chose Flash and Heal. Now, you might be wondering : Why noob Heal?. Well let me explain that.
I chose "Noob" Heal because you dont really need ignite if you've got your sniper in your hands.
Get it? USE YOUR ULT IF THEY ESCAPE!!!
I could still recommend ignite but its better to use heal.
Flash is obvious, no need to explain that.
You could use ghost, exhaust or Cleanse to chase enemies or escape them BUT its better for the support to use exhaust, because he is the support!

All in all: Caitlyn is a GREAT ADC but doesn't have loads of health.
She can really do some sirious damage and destroy the enemies.
Play offencive but not too offencive. If you run out of mana alot, you are playing her wrong OR you just really need blue buff.

AND THE MOST IMPORTANT OF ALL: BE FRIENDLY!!!!