Caitlyn's secret to optimizing damage output is to balance attack damage and attack speed in light of her passive. All too often I see people get one or the other, or some broken medium. This is really all item dependent, which is farther down the guide.

The other thing is that Caitlyn is actually an extremely DIFFICULT champ to play. Yeah, RIOT says she is "medium" but like Ashe, she is simple to play, but takes hard work to master. To master her you must know how to position in fights to avoid damage, position to utilize Q and R, use traps during fights and to zone the enemy, use E for more than jumping walls, and the list goes on.

Ghost and Flash are a basic combination for an Ashe-like carry that has minimal escapes. Ignite is not recommended since to use it you are negating Caitlyn's range bonus. I do not suggest using anything other than Ghost/Flash. Period.

Runes, combined with masteries, grants 31 armor pen at level 1. This is pretty much true damage to most non tanks and people that don't have armor runes or a cloth armor at level 1. This means harass early and hard!

Not your typical 21/0/9 build, look closely. At first some might scoff, but let me explain. (1) Caitlyn is incredibly dependent on early, fast farm. 2 points in Offensive Mastery for additional damage to minions makes farming easier and more effective. (2) 4/4 in Alacrity, which is usually 2/4 is important because attack speed to Caitlyn is so crucial in getting the most out of your passive. Thus, getting only 1/4 in Sorcery and skipping Archaic knowledge, we prioritize Caitlyn's strengths early game (farming) and end game (physical damage).

I start at level 1 with Yordle Snap Trap (W). A lot of guides ignore this ability to really late in the game, which is utterly wasting one of her greatest abilities! Get rank 1 W and run to lane and trap bushes to begin with. After they trip them checking bushes you have options to continue trapping bushes, wall off the river gank lane with traps, or use them to zone your opponent. Mastering the use of traps both during combat and setting up for combat makes all the difference in a good vs bad Caitlyn.

Here are some good places to put traps!
The light blue, green, and yellow on the top/bot lanes indicate great lane positions for traps. They can cut off ganking late completely, force your opponent closer to the brush (good for passive ability use), or keep them out of the brush.

Yordle Snap Trap Map!

The red dots all over just indicate good scouting places for traps and places to setup escape/gank routes or to cover dragon. The yellow in mid shows how you can block a lane off, forcing the enemy to either take the skinny path between the tower and the wall, or eat a trap. Great to force them to line up for a Q shot and for your party to take advantage for fleeing.

This is one of the most important things, and where most go wrong. To start off, if you get Last Whisper, you fail. It's a terrible item. If you want armor pen, get Black Cleaver or Ghost Blade, seriously! The way the math is calculated (which I won't go in to) makes the 40% on last whisper at best something like 30% if their armor is between 50-100. To make it worse, having flat armor pen, makes Last Whisper less efficient, and it already has horrible stats compared to Black Cleaver as an end game item anyway. The fact is, by the time you can afford a Last Whisper, it's no longer going to give you 100% of what you paid for it. On the other hand, Black Cleaver will always gives scaling 30% attack speed, dmg, and flat (superior) armor pen. Besides, you are there to kill weak targets, not tanks. Your base 31 + Black Cleaver is enough to set anything but a tank to 0 armor. I haven't experimented too much with Ghost Blade, which may have potential as a replacement for BC. However, BC is so cheap and easy to get!

The core items (zerker greaves, cleaver, PD, infinity edge, blood thirster) should remain as such, however what you get for your 6th item really depends. I will often get a Quick Silver Sash, since it's good against basically every champ in the game, and removes ignite and all those dots they will toss on you because they know they can't get close to damage you.

The other option is a 2nd Phantom Dancer. I only advise this if the game is horribly 1 sided and/or they have really limited ability to disable (e.g. no Malz, WW, TF, Ashe, etc.) You can argue for another Blood Thirster, but kiting and positioning is so important, that I favor a PD; it also has better synergy with your passive and I believe gives overall more damage.