Here is a quick and working guide to dominate the bot lane with Caitlyn. My guides arent in-depth guides so if you want everyhing explained from the roots dont bother to read.

If you are laning with Nunu you can think about changing your flatt ad marks into 15% attack speed.
Armor pene marks are something you can think about too.

I've played with these masteries myself, and I recommend them to everyone else also.

I heavily recommend starting with Yordle Snap Trap , it brings good awareness into bushes if you are laning agains some heavy cc champion like Alistar , Leona or Taric. And ofcourse I would pick Piltover Peacemaker as my second skill to ease farming and to help harassing your opponents. Now when you have your Yordle Snap Trap and Piltover Peacemaker you can try and comboharass their support in the bush my inserting your trap, and when the support comes and clears it out just hit him with your Piltover Peacemaker. Not much to say, the skill will speak foritself, Ace in the Hole. One of the best adc ultimates there is. Makes killing low health enemies easy, or you can just poke them out of your lane, simple as that.

For summoner spells I would usually go with

Flash and Ignite
but you can also pick
Flash Barrier
Flash Cleanse , depends on which lane you are against.

Has one of the longest ranges
Traps can be used as small wards if positioned right
His net gives him a good escapemethod
Strong pusher

Not so much sustained damage as other ad carries

Farming is the main thing you want to focus on your lane. You can win your lane entirely with farming if you manage to outfarm the other carry. Definetly something you want to focus and get better on.

When you are playing rankeds I recommended strongly playing with Nunu & Willump or Sona