Caitlyn is the sniper of League of Legends. She poses a big threat due to her high damage and range. This guide will outline a "sustainable" build, building normal AD and AS, but also adding in plenty of life steal, and above-average armor/magic resist.

There is one golden rule that applies to everything in life, and remains true with Caitlyn:
"Always press your advantages."
Caitlyn's main advantage is her range: always always always attack from a distance, pressing your advantage and winning the game.

Pros:

• Very high range
• I mean EXTREMELY awesome range
• Very high damage
• Harassing and farming are SUPER easy and effective
• Viable gank escape methods

Cons:

• Incredibly squishy
• Effectiveness decreases as game progresses
• Very high mana requirements

In other words:
SOLO LANING WITH CAITLYN IS EXTREMELY EASY.
Seriously.

You start the game with a basic sword and a health pot. "NO UR SUPOSED TO START WITH DORANS BLADE OMG NOOB". No. Doran's blade, while it helps in the start, is not economically strategic. Whaa? You can't build it into anything, and end game you are forced to sell it, at 70% of the original price. 475 * 0.7 = 142.5 gold. That is gold you just wasted. You could have bought 4 health pots with that. So why waste money? Plus, the 80 health and 3% life steal is hardly noticeable, and it is far more efficient to buy 4 more health pots than a doran's blade.

After you lane for a bit, you should head back and get a vampiric scepter. You are around level 4 by now, so you are probably dealing about 60-75 damage, depending on which runes you got. Hitting at about 1 hit per second, this is like a 70% potency health pot, going all the time. Pretty useful.

Next, you want Berserkers greaves. 25% higher attack speed? Yes please. That's 25% more damage and 25% more healing from the scepter. Also added movement speed is always good.

It's about level 6, and people are going to start getting their ultimates, and of course ganking more. You are still squishy as hell, so you really need to build your magic resist. AD resist is not as important because they normally cant get to you, you're too far away. So, buy your way to a Hexdrinker. You will worship this item and the 250 damage shield it gives you. It will also boost your damage and magic resist, so all those APC's can go bye bye.

Your damage is still significant at this point, you're dealing about 100 every hit. So lets boost that up enormously and grant lots of lifesteal with an Executioner's Calling. 15% crit strike, 18% life steal. You will be dealing like crazy and healing like crazy. As a bonus, you will deal 32 damage over 8 seconds every time you hit someone with a basic attack, and you can use the active, which works great on escaping enemies who you can finish off with your ultimate.

So your lifesteal and damage are good... now what? MORE DAMAGE. Build an infinity's edge, and your dps will go soaring through the roof. You then build a Maw of Malmortius, for even more damage and magic resist, plus that nice passive.
IF YOU ARE BEING TARGETED BY ENEMY APC'S BUILD THE MAW FIRST, THEN THE INFINITY'S EDGE.
That extra magic resist will help lots.

There is no ADC without a bloodthrister, so get yourself one of those. Your damage will go through the roof and as will lifesteal.

Finally, get a Madred's Bloodrazor. Not only will you deal more damage faster, you will also deal a percentage of the target's health every hit and get lots of bonus armor.

If your enemies are building with lots of armor, consider getting a Last whisper instead of the bloodrazor. If you can allow it to yourself, a black cleaver will also benefit a lot.

If you feel like you are losing too much health, consider buying a Tiamat. You should definitely get it if you are laning in bot: You could score a double-hit on enemy champs and it will help get you more CS.

Going over the abilities is silly, just look here: http://na.leagueoflegends.com/champions/51/caitlyn_the_sheriff_of_piltover

This however, this is not:

Order of priority:
-Ace in the hole
-Piltover Peacekeeper
-Yordle Snap Trap
-90. Cal net

Some tips:
-Place yordle snap traps at brush entry points. Try to avoid placing them in the brushes along mid, it is too big a brush to even hope for a hit. A great place is the little brushes near dragon and baron.
-Use your E to perform a mini-flash. Aim it opposite to the direction you want to go. You can even jump over walls with it, saving precious time in chases and getaways.
-Your W gives you momentary vision: you can use it to check nearby brushes for traps or even enemy champions.
-Placing all 3 traps side by side in a lane can be very effective: enemies have to explicitly aim through, slowing them down and allowing for easy Q and auto attack hits.
-Hitting from brush counts as 2 stacks for the passive. Math time!

IMPORTANT

When attacking from brush...
Every 4th attack deals 250% to a minion. 100 * 3 + 250 = 550. 550 / 4 = 137.5.
Attacking minions from brush increases damage by 37.5 percent.
Every 4th attack deals 150% to a champion. 100 * 3 + 150 = 450. 450 / 4 = 112.5.
Attacking champions from brush increases damage by 12.5 percent.

When not attacking from brush it is every 7 attacks.

The point has been made... always attack from brush if you can. If you're taking blue or red, please... 37.5% is ENORMOUS.

Runes:
Pure damage runes are the way to go with this Caitlyn build. Get the flat damage ones - they make for better early game which again, presses her advantages. It will deteriorate from end game, but early game is where you are taking hold of the match with an iron fist. Press your advantages.

Masteries:
22, 0, 8. Why not 21, 0, 9?
Because you want that magic pen for your bloodrazor, executioner's calling, and abilities.

Exhaust - Good choice. Makes nearby enemies regret hugging you.
Ghost - Meh choice. Could be useful in a getaway.
Heal - Not needed. You should have plenty of lifesteal to always be up.
Revive - Early game where you are most important death times are low. Thus, not important.
Smite - No...
Surge - Not particularly useful... you are not AP.
Teleport - Caitlyn is a slow champion, this is a good choice if you want to get around faster.
Cleanse - Not very needed... you should never be the focus of the enemy team, anyways.
Clarity - You are an ADC, not an APC. You shouldn't rely on mana to deal damage.
Ignite - Good choice, but not very practical. You would normally be too far to use this.
Promote - Not a bad choice, use it before you leave lane and b.
Clairvoyance - Leave this for the support
Flash - Always a good choice.

Best summoner spells to use: Flash, Exhaust, Teleport, Ignite, Promote.

A note about Promote: I always say to press your advantages. Promote will help early game so much, you will EASILY shut the enemies down right off the bat with Promote. Many people underestimate its powers.