I'm a Platinum ADC main on the NA server whose main champion for ranked play is Caitlyn
Why pick Caitlyn?

She's an extremely safe pick due to her long range, waveclear, and escape. You first pick her every game without worry of being countered. Her kit is geared towards early game, so if you ever want to get fed but feel you're like me and not very good at laning, Caitlyn is probably the way to go.

FOR CHAMPION MATCHUPS HOVER OVER THE CHAMPION ICONS ABOVE FOR INFORMATION

Starting Items

Doran's Blade is the best choice for ADCs, gives AD to last hit, HP for more survivability and the changes mean the 3% lifesteal will now scale with you throughout the game, allowing you to skip the Vampiric Scepter.

Build Path

2x Doran's Blade gives a lot of early game power. The Doran's items are extremely cost efficient and cheap. Getting a second Doran's Blade should also give you enough life steal to skip the Vampiric Scepter and go straight for an Infinity Edge.
While Doran's Blade is extremely cost efficient, it can't be upgraded. Building more doran's items allows you get an edge over opponents who buy similar costing items which can be upgraded, but doran's items will slow down your build. If you're snowballing, you can skip a second Doran's Blade and buy your Infinity Edge since you have the gold and lead in lane already. If you're losing lane though, you might find that your lane opponent is much stronger than you or you can't afford the components for Infinity Edge. In order to compete in lane while that far behind, you might need to get a third Doran's Blade. For all other purposes, a second Doran's Blade will allow you to extend your advantage in lane without setting back your build too much.

The early Vampiric Scepter buy is actually inefficient in my opinion. Since Doran's Blade gives lifesteal now, I don't really see the point in wasting 800g on 10 AD and 8% lifesteal. It's really much better to just buy a B. F. Sword and begin building the Infinity Edge. This is especially true for Caitlyn, who shouldn't really have much trouble winning lanes without needing lifesteal. The reason I recommended an early Vampiric Scepter however is, I'm assuming that people reading this guide will be new players, inexperienced in either ADC, Caitlyn, or both. The early Vampiric Scepter will help learning players to survive in lane and gives a much more easily reached goal of 360g + 440g than 1550g on the 1st or 2nd back for new players who might have trouble farming. I personally build my Vampiric Scepter after finishing my core build and choose to build an offensive item.

Zeal is a great item, Attack Speed and Crit Chance for more damage, Movement Speed for more survivability (kiting), all for 1100 gold. The big question is, what do I upgrade it into? My answer, Phantom Dancer is obviously better on pretty much any ADC. HOWEVER, if you can afford a Statikk Shiv but not a Phantom Dancer, then buy the Statikk Shiv. It's much better to finish an item than to just have the components for a slightly better item. Another thing to consider, if you have a low waveclear (can't kill minions very fast) team such as, Trundle Elise Nidalee Caitlyn Braum, a Statikk Shiv could help clear those waves and potentially save your tower or help kill theirs.

Offensive Items
With the new 4.12 Bloodthirster, I feel this item became the better one for Caitlyn to build. Improved lifesteal and AD means more safety, more Piltover Peacemaker damage, and faster turret takedowns than the Blade of the Ruined King for extended sieges which Caitlyn is so good at. I've also never been too fond of how dangerously close you had to get to use Blade of the Ruined King's active on Caitlyn.

But what about Runaan's Hurricane?
Please never build this item unless its ARAM or something. The last thing Caitlyn needs is waveclear. She does need the attack speed and the bolts create an interesting interaction with her Headshot, allowing her to get 3 stacks at once. However, building a Runaan's Hurricane means you have to replace an item, either Phantom Dancer, losing the survivability from the movement speed and damage from critical chance, not worth it, Blade of the Ruined King, losing the survivability from the active and life steal, and the damage from the AD and passive, not worth it, or a defensive item such as your Guardian Angel, which could be worth it, but if you're ahead enough to buy a Runaan's Hurricane instead of a defensive item, you probably won already and might as well just buy a Bloodthirster to snowball your lead with 80 AD, a ~400HP shield, and lifesteal.
My main gripe with this item is that its passive has far too low range. Its exceptionally dangerous for ADCs, especially Caitlyn, to be in range to use the passive of Runaan's Hurricane without being destroyed by a tank or assassin like Renekton or Fizz.


Defensive Items
GUIDE TO CHOOSING DEFENSIVE ITEMS:

Guardian Angel Is good for when you absolutely need to live, but they have way too much burst or focus on you. Its also good if someone else on your team is strong enough, Jax or Kayle for example, to wreak havoc in a teamfight while you're reviving after being focused.

Mercurial Scimitar Is good for when they have a champion with some kind of heavily focusing skill, such as Warwick's Infinite Duress, Skarner's Impale, Zed's Death Mark or Malzahar's Nether Grasp. All 4 of these ultimates will pretty much kill an ADC like Caitlyn, but can be completely removed with the use of a Quicksilver Sash or Mercurial Scimitar.

Randuin's Omen Is a situational item for sure, but if they have a fed AD champion that can dive you repeatedly, Randuin's Omen gives the health, armor, and self-peel to potentially survive against champions such as Fiora, Talon, Tryndamere, and maybe even Master Yi.

Banshee's Veil Is a great item if there's just one incredibly dangerous skill on the other team you need to dodge such as Malphite's Unstoppable Force or Annie's Summon: Tibbers.

Flash and Heal are the two summoners that will help you survive the most. As an ADC, its your goal to keep on living and dealing damage. There's not much else to say about it. You can also take Exhaust instead of Heal in some situations if your support takes Heal but I don't really recommend it.

11 AD is what you need to easily last hit under tower, however Caitlyn doesn't usually get shoved under tower so you could choose to get a 3rd Greater Quintessence of Attack Speed if you plan to just shove the wave with Piltover Peacemaker constantly.

Not having any AD however, makes it extremely difficult to last hit unless you're amazing at it, which is why you should always run 9 Greater Mark of Attack Damage. Unless you're feeling lucky, then you can run 1 Greater Mark of Critical Chance and 8 Greater Mark of Attack Damage.

With the buff to champion base armor, Greater Seal of Health has become the go-to seal for survivability in my opinion, since the bonus health + base armor gives a great combination of stats against the ADC and usually magic damage Support. I originally ran 9 Greater Seal of Health but I received a comment advising to run mixed Greater Seal of Health and Greater Seal of Armor, I decided to make the change since after looking at it, the effective HP is high using 5x Greater Seal of Health and 4x Greater Seal of Armor.

Attack Speed helps Caitlyn win trades, not only by getting more attacks off, but by making your passive Headshot come up more often. You could do without the 4 Greater Glyph of Attack Speed though and replace them with 4 Greater Glyph of Magic Resist or 4 Greater Glyph of Mana Regeneration if you plan on using your Piltover Peacemaker a lot.

Double-Edged Sword Isn't worth it for ADCs IMO, your goal is to survive and even if you deal more damage, you don't exactly have the tank stats to survive from getting dealt even more damage.

Fury Gives Caitlyn attack speed to trade better and get Headshot stacks faster.

Butcher Helps with last hitting and gives access to the Feast mastery which gives Caitlyn more sustain in lane.

Expose Weakness Allows your allies, usually your support, to deal more damage onto a target when they get hit by your skills, usually your Yordle Snap Trap or Piltover Peacemaker. A decent mastery for harassing in lane.

Brute Force and Martial Mastery give you AD, which of course, you need as an ADC.

Executioner is an amazing mastery, free damage onto your targets with low health.

Dangerous Game just might save your life in a fight, the heal is pretty significant so I'd recommend always taking this mastery.

Warlord is a pretty useless mastery even for an ADC in my opinion. It just doesn't give very much AD and its useless early game so I only put 1 point in it because there really wasn't anything better.

Frenzy Free attack speed on crits to get more Headshots are always good.

Devastating Strikes Increases your damage output and its actually a pretty significant amount of armor pen.

Havoc Free damage, 3% is a lot of free damage too for 1 point.

Block and Unyielding are pretty generic masteries, very useful since every champion autoattacks.

Recovery gives you some HP back if you ever take damage, better than the alternative, Enchanted Armor , which I absolutely hate and think no one should ever take since it doesn't give you anything really, I mean 5 armor at 100 armor is pretty useless, especially for an ADC who builds almost all offensive items.

Veteran Scars and Juggernaut are 2 more very generic but very useful masteries for helping an ADC survive.

If you really plan on spamming your Piltover Peacemaker, you could also take some points out of Veteran Scars and Juggernaut for Meditation .

Piltover Peacemaker is by far your best skill, it gives poke and waveclear, the reason why Caitlyn is so strong in lane. Use this skill to shove your opponent under tower to make it harder for them to farm. It also can help you win trades since by clearing minions, your minions will be attacking their ADC during a trade while they have no minions to attack you. Take this skill first against champs who generally have no response to being shoved at level 1, such as Ezreal, Twitch, or Vayne. Max this Piltover Peacemaker first always.

Yordle Snap Trap is an extremely useful skill for protecting yourself from jungle ganks or zoning the other ADC from farm or fighting you. Place your Yordle Snap Traps around the other laners' tower to make it much more difficult for them to farm since if they try to dodge poke from Piltover Peacemaker, they might walk onto a Yordle Snap Trap and take a ton of damage anyways. When trying to take an objective such as a tower or dragon, place these traps under you so when an initiator on the other team like Xin Zhao or Vi tries to catch you out, they'll end up trapped and you can get away rather easily. Take this skill first to gain knowledge of early game invades and bot lanes trying to zone you from a bush. Try your best to place your traps under targets who already are immobilized by skills such as Morgana's Dark Binding or Thresh's Death Sentence in order to chain your crowd control effects. Maxing Yordle Snap Trap second gives Caitlyn more damage on her traps and lets her replace triggered traps more often

90 Caliber Net is Caitlyn's safety tool, offering a slow. You shouldn't need to use this skill twice in a fight since Caitlyn's range means her positioning should always be good enough that just one 90 Caliber Net saves you from a dive. You won't be using this skill for damage either, so there's no real need to max this skill right away.

Ace in the Hole is a great skill for securing kills. Please, never, ever use this skill when you're in autoattack range. It does a lot of damage but your Damage Per Second in comparison to just autoattacking is much lower. Don't bother using this skill if your target is near teammates either, they'll just bodyblock it and you'll have pretty much wasted your ultimate. If you ever see their carries alone, especially carries with no sustain such as Veigar, use Ace in the Hole on them to scare them off the next fight, making the next fight easier since their carry starts with significantly less health or just aren't in the fight because they need to heal. Put points into this whenever you can.

For individual champion matchups, hover over the champion icons near the beginning of the guide for my advice.

Laning Phase
Despite being strong in lane, Caitlyn will actually lose most 1v1 fights against other ADCs. Her strength comes from her range allowing her to fight other ADCs without them fighting back, and her Piltover Peacemaker which allows her shove the wave while harassing the other laner. As Caitlyn, you should always try to stay at max range away from the other ADC, and shove them to their tower where you can freely harass them while they desperately try to farm. I'd also like to mention, if you ever do get engaged on by something like Graves' Quickdraw or Lucian's Relentless Pursuit, you can use 90 Caliber Net on them, and while in the animation of flying away, use Piltover Peacemaker. The result is, you fire Piltover Peacemaker after escaping with 90 Caliber Net however, Piltover Peacemaker is fired from the position you used 90 Caliber Net from, not your new position, letting get harass off while escaping.

Midgame
After you've taken the other laner's tower, you can begin roaming, try and help lanes that are having trouble and take their towers too. If nothing is happening (Its not safe to continue pushing, or no one is grouped), just find an open lane and farm. Farming is extremely important as an ADC since it helps you get your items to dominate teamfights. However, look on the map, if your team is all walking to one place, chances are, they all want to do something. Do not neglect your team for more farm, go to help them with their defense or siege. There's no point in being fed if you don't fight.

At this point in the game, teamfights will start to happen and I'd like to explain how to teamfight as Caitlyn. STAND AT MAX ATTACK RANGE FROM THE ENEMY. Like I said before, Caitlyn will lose 1v1s to just about any ADC. You don't need to focus their ADC, their APC, or whatever your team says to focus. You, as an ADC, should just worry about staying alive to constantly deal damage. I don't care if the front of their team is a fed Vayne or a feeding Renekton, just focus them from max attack range and you'll be doing your main job of dealing damage AND NOT DYING.
Also, with all these champs trying to dive you, kiting becomes essential. Don't just stand there autoattacking while they kill you. After you see the bullet come out of your gun, right click where you want to go, then count out how long it takes for your next attack to come out (One second divided by your attack speed), and after that time is up, auto attack again, then when the bullet comes out, you know what to do. Using Shift + Right Click or A + Left Click (Attack Move) might make this easier for you so try it out in a custom game or something.

Lategame
Pretty much the exact same advice from before, but now I'd like to add some more advice. Don't push out too far. Midgame, everyone is spread out so its usually safe to farm since you have vision of everyone else, but late game, if you have no vision of the other team, chances are, they're coming to kill you while you're separated from the team, and a dead ADC at 40 minutes is almost always a lost game. Just stick with your team 24/7 and you should be fine. I'd also like to advise you and your team to stay away from bottom lane after about 25-30 minutes since if the other team sees your team at bot lane, they'll almost always go for a free Baron, putting your team at a severe disadvantage in the next fight.

This trap can be used to spot early invades or jungle ganks if the jungle walks into the bush. Its not very reliable though as the jungle might walk around it, so be careful.

Another trap that can spot jungle ganks, this one is set off surprisingly often.

A trap near the edge of a bush can bait the other laners into walking into it if they lose vision of you walking into a bush.

Its very common for ADCs to stand around there while farming since its so close to the safety of the tower. Placing a trap around that area will zone the other ADC from their own tower, forcing them to lose farm or risk taking harass from you, who's out of turret range, while farming.

Please never go this way, its a guaranteed way to get hit by skillshots, if the other laner tries to run away from your team, running this way will lead to some heavy damage. It also gets rid of the shenanigans where someone tries to run in circles around a tower, kiting the person diving them.

Multiple traps under turret make it near impossible for an ADC to farm without taking harass from you. Be careful about this though, since if the wave leaves the turret, your traps are likely to be set off very quickly by the support.

A trap under your feet while sieging a turret will CC anyone trying to dive you.

Also, if you ever see someone teleporting in, put a trap under whatever they're teleporting for to make sure they don't do anything for a while.

Thanks for reading my guide, please leave a comment telling me what I could do better and what I should I add to my guide. Good luck in your games and I hope I was a help.