Introduction.

Caitlyn is a long-range DPS AD carry which can cause huge amount of damage in seconds if played correctly.
She is not that difficult and very strong to play and can carry the game later on.

Runes.
I personally give Caitlyn some AD runes for early game (+9 damage) and a significant amount of attack speed. The reason i do this is because of her passive. The fact she has the very long range ability makes her exceptional in harrassing out of lane and keeping enemies champions in distance so they can't get experience from creeps.

Masteries.
21-0-9
Getting as much damage as possible to get to the last mastery of the Offensive tree.
Giving also 9 points on Utility for Movement speed,limiting the durations she is dead and relic for red buff when possible.

Items.
Standard AD carry items including Frozen Mallet when chasing enemies and Guardian Angel to make you last more late game.

Skills Sequence.
Taking a point on trap and Net and maxing her Q for harrasing. Of course taking Ultimate when possible.

Summoner Spells.
To be honest on Caitlyn i prefer ghost rather than Flash as i can chase enemy champions or getting ASAP close enough to cast the ulti on low healthed champions.
Heal can make you last more and with a communicative team there is a high chance of winning the game.

EXTRA:
Ranked play.
Caitlyn is a very strong AD carry as i mentioned in the introduction.
Of course in a cooperation with a good support like Taric (for stun), Soraka (for mana and heal) or Janna she can take down enemies too easily in early-mid game.

Creeping/Jungling.
Jungling is out of the question for Caitlyn. As for creeping and getting CS its very easy in bot lane along with harassing.

Farming.
Check Creeping/Jungling ;)