Well, I'm not too sure what to write here but here goes.

I would like to note that i have changed this build with the advice from some comments, Thank you for those.

Firstly i would ask that you do not judge my build before you try it for yourself.

I suppose i should explain the build order for you, I start with boots of swiftness because cait needs all the help she can get to escape, The black cleaver is a good second item because of the attack speed and the damage (not to mention its passive which is a big help in early team fights.) After this i use the Phantom Dancer, the extra attack speed should now make you fast enough to bring down other squishy heroes with ease. I bring the bloodthirster in now because it can give you up to +100 AD, the lifesteal is good, but don't rely on it, cait is a squishy hero and lifesteal or not if you are targeted you will die, but again it will let you kill all your squishy enemy's. After this i bring in Madreds, With this you should now be able to drop most enemy's as long as its 1 on 1 and you will be putting out alot of dmg in the team fights. I Finish off by selling dorans blade for thornmail / Force of nature depending on the enemy team, Thornmail will allow you to survive a bit longer and the passive will really help when you are targeted.

As caitlyn do you are very squishy so make sure to use your 90 caliber net when being chased, this is also why i have chosen ghost as a summoner spell.
Early game Pitlover Peacemaker is a nice move to harass and pick up minions kills, If you are attacking a tower, use it on a minion line while they are moving towards you to weaken them, then finish them off to continue pushing the tower.

Caitlyn's skills can be quite useless late game, other than Ace in the Hole, but try not to use this unless the enemy is alone and on low health, otherwise another enemy may intercept.

I have found this build very fun to play, and it is usually very successful for me.

I should explain that i am not very good at writing guides, i have made this mainly for feedback on my build and in the hope it might help some people.

At times following this build exactly wont be much use to you, They enemy will probably target you in team fights and if you are struggling to escape some armor such as thornmail or force of nature might be your best bet. Also if you like life steal you could always remove a item for a second bloodthirster.

I only used these summoner spells because it made me pick two, but i would suggest just using the two you have the most success with.

Try not to initiate team fights as cait, and stay as far back as possible, use your range to your advantage. If the enemy team does not recognize you as a threat you will have some fun proving them wrong.

Once you have madred's blood razor you will watch even tanks like Dr Mundo drop fast, but try not to get too cocky, i did when i first started using this build.

I would like to point out that i found this build by experimenting, and i understand it is not for everyone. But i will be constantly changing it trying to improve. and when i think i have found something worth changing i will update this build.

Right now i am just trying to reach the 5k character mark so i am using this line to fill some space.

If you like this build please vote, Also leave comments to help me improve this guide, I am aware it is very basic and needs touching up.

Thank you for reading this.

One of the reasons Piltover is known as the City of Progress is because it has an extraordinarily low crime rate. This hasn't always been the case; brigands and thieves of all sorts used to find the city-state an ideal mark for plunder, primarily due to the valuable resources it imports to fuel its techmaturgical research. Some even theorize that it would have fallen long ago to the chaos of organized crime if not for Caitlyn, the Sheriff of Piltover. Born the daughter of a wealthy statesman and a pioneering hextech researcher, Caitlyn discovered her natural gift for investigation when, at age 14, her father was assaulted and robbed on his way home. She snuck out of her house that night with her father's rifle and tracked down the muggers from the crime scene. At first, her parents did their best to discourage her from such risky hobbies, but she was incorrigible. Wishing to protect her daughter in the only way she knew how, Caitlyn's mother began outfitting her with techmaturgical devices tailored to her sleuthing needs.

Caitlyn quickly gained notoriety, both because she was single handedly defeating crime in Piltover and also because she soon developed into a ravishing beauty. She never backed down from a case or a challenge, and she was one of the sharpest shots in the city-state. Her services were soon requested by Demacia to help track down a mysterious outlaw who had begun committing high-profile heists. The bandit, who always left a card with an ornate 'C' at the scene of the crime, became Caitlyn's arch-nemesis. To this day, Caitlyn still searches for this cat burglar, and the chase has led her all across Valoran. She has joined the League to hone her skills and gain the influence necessary to track down the only quarry that has managed to evade her.

Damage: 47 (+3 / per level)
Health: 390 (+80 / per level)
Mana: 255 (+35 / per level)
Move Speed: 305
Armor: 13 (+3.5 / per level)
Magic Resist: 30 (+0 / per level)
Health Regen: 0.95 (+0.11 / per level)
Mana Regen: 0.8 (+0.07 / per level)

Pros
-Excellent farming skills
-Great damage dealer
-Using your passive correctly leading to line control
-Can kill low-hp enemies in a great distance
-Smart chaser with the 90 Caliber Net skill
-Can change the outcome of a team fight if positioned correctly
-Can take on both mid and top/bottom line cause of the bushes
-Great range (650) for tactic 'hit and run'

Cons
-Very squishy
-Can't do much in teamfights
-Target in team fights
-No reliable escape tactics
-Skills are partly useless late game
-Very low mana pool
-Her traps are visible
-Easy to counter, by stacking armor
-Ulti can't be reliable because enemies can interrupt it if they step in front of target