Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
(Solo Lane is first build, Supported is second)
(If you're wondering why I do not have a full item build please scroll down to the Masteries, Skills, Items and Laning Chapter.)
Since this is my first guide ever I think I'm going to keep it short.
This is a very basic guide to Caitlyn, The Sheriff of Piltover. I went through several of the guides on Mobafire, comparing my build to other guides, and found that not many of them were up to date on how Caitlyn should be played. So I felt a very basic guide only detailing build, skill sequence and basic laning style could be helpful. (Though if people want it I can go into more detail about each play style)
Two different styles of play will be addressed in this guide, a solo lane Caitlyn, and a duo lane Caitlyn supported by either, Sona, Soraka, Taric, Janna or Karma (personally I feel Soraka and Janna are the best supports for Caitlyn.)
So here it is my rationale on why Caitlyn is an extremely powerful and viable carry in League of Legends.
If you don't like my build or masteries I'd suggest trying this guys build and masteries.
For the solo lane we're using heavy armor pen runes, mana regen, and your personal choice of blues, I find magic resist to be the most useful because you cannot afford to buy magic resist early in the game, (other then a Null Magic Mantle). The armor pen quints can be swapped out for flat health or movespeed quints. The only truly necessary runes are armor pen reds and mana regen yellows. These are needed to be able to use your abilities and auto attacks to their maximum effect.
In this lane it is actually better to have flat attack damage runes. This is to counter other support/carry lanes and to make your pushing stronger. It is not uncommon for a good Caitlyn support lane to be able to push down a tower in less then 10 minutes if they aren't interrupted. Other then that the runes are more or less the same; mana regen and your choice of blue runes. I would highly suggest keeping the armor pen quints however, because against tanky bottom lanes they become very useful.
Caitlyn has a fair amount of flexibility when choosing runes. The only strict guidelines I would follow would be to always have at least 15 armor pen at level 1, either from runes or masteries + runes.
Masteries, Skills, Items, Laning and more!
In a solo lane your job is to harass your opponent, farm and to not get yourself killed. Caitlyn already has several decent ways of foiling ganks and defending herself from her opponent in lane. The support masteries and boots + pots at level 1 provide you a good amount of mobility to use to escape ganks and to harrass your opponent freely. Remember, you will almost always have a harass advantage against any champion until level 6. Make the most of this time and harass hell out of your opponent before they can become strong enough to resist you.
For a Caitlyn with a support its all about the damage you deal. In a duo lane you have two people to harass and someone will be most likely healing you or shielding you (or both). In this situation you need more damage to be able to quickly kill minions and be able to wear your opponents down fast. This is why taking offensive masteries, (Havoc still isn't worth it, the bonus mana regen from support is better,) will benefit you more then support masteries. The critical strike damage mastery is not actually necessary, (the points can be put into reduced CD or magic resist/armour,) but can be helpful later in the game.
For skills I always take Yordle Snap trap first, then level my Q. It is more useful at level 1 then your Q or E. Use it to, block off a portion of your lane, protect your jungler, reveal their jungler and protect yourself from ganks. Since this skill has been changed to 3 traps it is by far the most powerful part of her skillset. Whenever someone steps on your trap and gets rooted, punish them for it. Auto attack them or Q them while they are rooted. Doing this is key to establishing your lane dominance. If you feel it is necessary take your E at level 3 instead of your Q, this won't hurt your laning.
(NOTE: If your lane is proving difficult to stay in for longer periods of time at low level, consider getting several dorans blades or a vamp scepter to increase your sustainability.)
For the items I put the core build of Caitlyn on the build part of this guide. Her last two items are always situational. Sometimes you require quite a lot of defensive stats, so a guardian angel and banshees is necessary. Other games you may just be rolling their team and want to grab a bloodthirster and another phantom dancer. Heres a quick list of good items for these last two slots, organized from most useful to least useful.
Cloak and Dagger
Bloodthirster (This or starks is almost necessary if the enemy team has several thornmails)
Phantom Dancer (Yes two phantom dancers is good, try it before you hate on it)
Frozen Mallet (Debatable, but it does provide hefty hp and works well with atma's)
Wit's End (Against magic damage heavy teams)
Madred's Bloodrazor (Only good against teams that are stacking huge amounts of armour or health. Last Whispers armor pen can deal with tanks that have less than 200 armour)
(The first two are the only ones I feel are really viable but others will work)
Force of Nature
Atma's Impaler (Requires Frozen Mallet or Banshees to be a good choice)
The only really viable spells are Ghost and flash. People may tell you otherwise but these two spells give you what you need most, mobility.
If you are completely against flash or ghost, teleport and exhaust are acceptable substitutes for either ghost or flash, but are not as effective.
Just to re-state this, this is a only a build/skill sequence guide not in-depth (yet)
Caitlyn does not burst as well as Corki, and does not have as much utility as Ashe. What she does bring to your team is an absolutely infuriating solo or duo laner that can easily shut down her opponent in lane and then snowball out of control if she is allowed to farm or gets fed.
Don't listen to people who believe that Caitlyn is useless later in the game. While it is true that Caits strongest points are early and mid game, that doesn't mean she can't carry easily. Her absurd range, excellent poke and short cool down traps make her an excellent team fighter if played correctly.
And anyway the only way your going to get better at a character is by playing them so get out there find your own way of playing Caitlyn. :P
Bonus (the troll lane)
Recently I found that a duo lane of two ranged carries that are harass happy is a great method of pubstomping. So if you want to troll a top lane solo take Caitlyn and Vayne and go top. Procede to completely deny said solo and push down their tower in a couple of minutes. Bonus points if the solo lane is a melee character like Akali. Be careful though because ganks can cause this lane to fail spectacularly.