On the first 3 levels get 2 times Piltover Peacemaker and 1 time 90 Caliber Net for maximum poke with Peacemakers. Max Q-Spell First then E-Spell and last your traps. Skill your ult normal on level 6,11 and 16.
Cait is the strongest ADC at Lane cause of her autoattack range. You can poke most of your enemys with autoattacks. If you get some expierience with Cait you will win most of your lanes. Work together with your support its important to ward for not getting caught. If Cait falls behind in Early Game she´ll have big trouble in Mid Game.
The Mid Game is the most difficult time for Caitlyn. If you got some advantage in Early Game you can splitpush on bot or top to farm up and get stronger and force the enemy team to split up. Teamfights are difficult with cait cause she don´t get all important items to survive. So care in the Mid Game to don´t get caught.
Caitlyn is strong in Late cause of her high range. Try to poke enemys down with autohits. Splitpush is a possible option in Late Game aswell.
In Teamfights try to stay away from the enemy team and poke with autoattacks if someone jumps on you use 90 Caliber Net to escapre and try to get as much autoattcks as possible out.