Hi all!

This is my first build, so I am open to any comments and suggestions!

I think that this is an awesome build for Cait. Full build and full stacks you will be attacking 2 times per second and each hit deals over 450 dmg, headshots will deal about 800 dmg, critical hits may deal over 2000 dmg and your ulti will deal over 1500 dmg at an awesome range! At this point in the game you could pretty much solo the Baron!

I recommend that you go with damage runes since they give you a lot of extra damage. If you want you may swap these damage runes for armour penetration ones since armour penetration can also help, especially if you are playing against champions with high armour.

As you can see I used the 22-8-0 Mastery Tree build since I recon that this layout gives you what you need although you can use any layout you prefer.

Most of the items you buy are for damage and attack speed. This is pretty much all you need to build for Caitlyn since you can use her range to stay on the edge of team fights, minimising the damage that you recieve.
Some people say that you should start with Doran's Blade since it gives you damage and health as well as lifesteal. It's a good point and they are right. Doran's Blade has more attributes than the Vampiric Scepter but I prefer to start with the Vampiric Scepter since it builds up into the Bloodthirster, which saves you gold and time.

The first skill that you want to master fully is the Piltover Peacemaker since it deals a decent amount of damage at a good range.
The second skill to master is the 90 Caliber Net. It can get you out of sticky situations quickly by slowing the enemy (dealing a little bit of damage too) and knocks you backwards to safety. You can also use this ability to catch up to any champions who are running away from you by shooting it in the opposite direction so that you are knocked in his direction.
The last skill that you master is the Yordle Snap Trap. In my opinion this skill is useless since unlike Teemo's Mushrooms and Shaco's Jack In The Box, it is visible and can be easily avoided by your enemy. The only way you can use it is either to slow an enemy which is chasing you or to check whether there is somebody in a bush.
Caitlyn's Ultimate skill, Ace In The Hole, is a unique skill which has an epic range which goes off the screen. You should use this skill to kill any low health champions who are running away in order to get an easy kill, although the shot can be intercepted by another enemy.

I use Heal and Ghost as spells since when you are low health, Heal always comes in handy (although late game your lifesteal will regenerate a lot of health quickly) and Ghost can always help you to escape any enemies chasing you, althouch you can choose any spells you prefer.

Early game you should farm a lot in order to level up quickly. By lvl 7 you may start to jungle a bit in order to earn some extra gold to buy the items of your build.
Mid game (after you buy the Phantom Dancer) you will start to get some kills but you should be careful since you are still a bit squishy and can be easily killed.
Late game you will have incredible damage and speed and you will be able to solo pretty much anybody.

I hope that you like this build! Please leave a vote and if you have any questions or suggestions feel free to leave a comment!