GET MIDLANE!
Yup, you defiantly wanna mid game as Caitlyn for several reasons
#1. She is very OP early game, defiantly a carry. She can solo lane quite easily too.
#2, Her range is un-matched. While There are a few champions with abilities that extend further than Caitlyns, you'll be hard pressed to find a champion with a longer auto attack range. You can harass and push back the enemy without using a single ability.
#3. Traps help prevent ganking. Mid lane is usually the first champion to get ganked once they extend too far. Well timed and expertly placed traps can prevent this.

Guide to mid-lane as Caitlyn.
Very important, get a health potion. Duh. You wanna start with doran's blade for that quick boost in stats, and a health potion, helping you lane longer without going back for health.
Stay at the tower till the minions march past, then move forward and auto attack minions. Simple right? Very. Continue to auto attack minions and avoid the other champion until you build up a head shot, then quick get within range and hit the other champion with it, run back, and attack minions again. Its like using a free ability to harass the opponent. While you can use Caitlyns piltover peacemaker to push the other team back, your going to want to save your mana for a few reasons. #1 being escape. If you fail hard, or the other team is just plain smarter than you, the 90 caliber net is amazing for running away. Not only does it launch you backwards, it slows the enemy it hits. When you get Caitlyns traps, place them as soon as possible in strategic locations to a). funnel the other champion to where you want them to go. And b). easy kill. While the traps do little damage, the snare the champion in place. Once this happens quickly with them with the peace maker and as many auto attacks as you can. If you don't kill them but get there health low enough, pop your ult and finish the job. And remember use her ult for LAST HITS ONLY! It costs double the mana of any of her other abilities, and does not do as much damage as you think it will. Trust me, you will be surprised how many times some one will survive her ult, but used right, you'll get a lot of kills with it.

At this point you should be a good way through the items, and have the peace maker at rank 5. You should have both your phantom dancers by now, which will give you a ton of attack speed. Now, sell your boots. Yes I know "Omg boots da bomb, you fail without them." Not true. Both phantom dancers will give you plenty of movement speed, and if you can't out run the enemy, well its your fault for over extending, because you should never be in that situation. Besides your net and traps make escape easy, no matter your speed.
Now that you have the attack speed, its time to get the damage to go with it. Start with the black cleaver, not only will it give you ever more attack speed, but it comes with a good chunk of damage, and the best part, its passive. You will burn down an enemies Armour is seconds, and then each hit is like using your ult, over and over and over....
Now remember, no matter how strong you get, you are still squishy. So STAY WITH THE TEAM! If you EVER run off to jungle while your team is else where getting spanked, you FAIL! You shouldn't even be jungling in the first place. with your attack speed you'll get all the last hits.

This is where the fun begins. At this point you may have noticed you do a lot more damage because of the black cleavers effect, making tanks a little less tough, allowing your team to take them down. Collaborative effort. Yay team work! But now its time to show everyone what Caitlyn can do. Get last whisper. You are now a tank Killer. I have personally gone 1v1 with several different tank champions, each with over 300 armor, and took them down in seconds. With the combination of your items you ignore 50% if not more of your opponents Armour. Your ult is still a huge asset, allowing you to take down the squishy guys as the hide behind their towers. Your peace maker will mow down a squad of minions, earning you all the gold you don't need.
but still, play it safe! You are not a tank yourself, so don't act like one.

With this build I have made some amazing scores as Caitlyn, and pwnd some serious newbs.
I highly recommend using this build if you are first starting out as caitlyn, I recommend it even if your a caitlyn veteran. But i also encourage you to try out your own Caitlyn builds and see how you do.
So to all the LoL players reading this
Good luck, and Have fun.

(any questions or comments feel free to message me.)