The early game on Cait is not that complicated, you have the great advantage of being able to tower in 5min or less. Cait has great harass and push with her q, and constant auto attacks means more passive harass on primary target.

Who should you attack in lane?

If the other team has an aggressive comp such as EZ/Taric, it would be prudent to be behind minions and to passive harass EZ as much as possible. Your support should be intercepting any move Taric(support) makes towards you.

In general it is a good idea to focus the ADC as it reduces overall damage because they are forced to commit or flee. However, some exceptions can be made, such as destroying an aggressive (squishy) Sona.

Once you have towered which ideally should be prior to the 15 minute mark (unless you are being countered/camped) you should be roaming once your lane pushes past the first downed tower. If the other team leaves lane you should continue to push to the second tower.

When roaming you should clear golems/wraiths prior to making your way to a lane. The idea is to not fall behind on levels/farm (which might happen if you are not in lane). Mid is the ideal goal for a gank as Mid + Cait's ulti should ensure an easy kill. Once you have killed mid, it should be an easy tower kill on mid lane if it is not already down.

Late game is tricky, as you have the choice of continually farming to stay ahead, or push and lose out on farm/exp.

Ideally by the ~30min mark you should be over 150 CS and halfway through the build. At this point you should have enough damage not to 3 shot people, but to generally do decent damage in team fights.

The main problem with ADCS is they have no idea where to stand.

When fighting one on one, you should be able to react quickly with an E on the target, and hopefully you have placed a trap and lead them toward it. Gain as much distance as possible, while at the same time spamming Q and auto attacking. DO NOT STOP RUNNING, YOU ARE SQUISHY.

In team fights your ideal goal is to focus ADC/MID's, however if they are smart they are also in the back. Luckily you have decent range and your Q should reach almost everyone. Try to position yourself behind Tanks and use your E to both gain/move into range of players you are intending to kill. Make sure you are aware of where your traps are, as you can always run to them for help.

In team fights Q should be a priority if you are hitting multiple targets. Your ulti should REALLY NOT be used until the end of a fight, as it takes you out of the game, and roots you in place. Ideally autoattack/Q should be enough to kill anyone you encounter.