I'm not sure what everyone else has heard, but pretty much everything I've come across about Caitlyn says that she sucks. In a way, that is true; however, in my opinion, every champion in League of Legends has the capacity to destroy the enemy. Caitlyn included.

First, I'll go over the masteries and runes. These two aspects of a build are really up for interpretation if you ask me. There are many options for this champion to include crit chance, attack speed, armor pen, attack damage, and more. I just chose the runes shown above because I believe they are good for any attack damage based champion. The item build adds plenty of attack speed, so I wouldn't go for runes in that realm. If I were to make every rune one single stat, I would go with armor penetration. On the other hand, if you grab a Last Whisper you won't need the runes for that either. The masteries I've chosen are also just sort of my basic attack damage champion build. I suppose you could add some magic regen runes and masteries, but I wouldn't advise it. Just use your abilities sparingly and rely on your auto attack for most of your damage. Your abilities should be more for harassing or when the right moment comes to use them.

On to the items...
From what I've seen in game, most players don't stack attack speed with Caitlyn. The way I look at it, if you want to use her passive to full potential, you will need quite a bit of attack speed. Then, when you add on the Sword of the Divine, you're basically adding another Caitlyn passive. When you're leveling up you will probably feel like you aren't doing any damage due to your low attack damage stat, but that speed is going to make your passive and the Sword of the Divine tear through your enemies. Plus, the little bit of magic damage from the Sword is going to bypass any armor the enemy is stacking if your team is heavy AD. Once you've got your first three attack speed items (boots, sword, at wit's), that is when you can start going for attack damage and/or armor pen. Usually, the game will be over by the time you finish your Bloodthirster, but if you have some time, feel free to pick up a Frozen Mallet or whatever else you feel will help with your particular game.

Early Game...
You are going to be staying in the back and laning with someone else: preferably a tank or someone who can take some hits. As always, focus on last hitting and harass the enemy whenever possible with your passive ability. Also, if you are going to use your Q to harass, make sure you conserve mana and get the creeps with every use. You're going to need lots of gold to be viable in a game, so those last hits and Q shots will need to bring you the dough. Overall, stay back, stay safe, and harass the S%$t out of the enemy.

Mid Game...
Not much changes from early to mid game other than the fact that you will be involved in more team fights. Your goal is to CONSTANTLY keep the damage coming on whoever you can. Pretty much everyone knows that you need to focus the squishy first, but because you are insanely squishy, you need to remain safe. If you charge in to attack the enemy squishy you will get focused like no one's business. Stay back, keep the auto attack on whoever is in safe reach (preferably a squishy) and keep your eye on whoever is lowest so that you can get an ult in before they run away. Your role throughout the whole game is to make sure no one gets away. If a low health champ starts to bolt for a tower, make sure you pop that ult. The tricky part is making sure no other champs are in your path so make sure you're also at a good angle to hit ONLY the champ that you are aiming for.

Late Game...
By now you should have your sword and wit's and be able to stay back and harass anyone who wants to get near your towers. You should also have a good feel for when to stay back and when to run in and deal that damage. Just keep that auto attack going and use your ult and Q to get those long shots in. Basically, DON'T DIE. You are extremely easy to kill, so don't get caught in the middle and don't get caught alone.