Greetings, derps and derpettes, today I'm gonna school you on how to build your ranged AD carry without having the world believe you're retarded. There's a TL;DR at the end in case you want to skip the reasoning and arguments and just want to learn how to build directly.
Things to avoid building first

- Phantom Dancer item Phantom Dancer first. If you build this first on an AD carry, you either just started playing a MOBA for the first time in your life, or you're in need of the angry god's fist of salvation. PD is an item that supports your damage, so for it to have any use, you need to build AD first. This concept should be easy enough to understand, but the number of people who don't get it and buy this item so that they can eat shit faster is astounding.

- Madred's Bloodrazor item Madred's Bloodrazor. Are you seriously building this first? This item is bad in almost any slot, to be honest, because the cost is huge for what it offers,absolutely huge. But that's not really the only reason why i'm millitant about it. This item gives percentile damage. Early game, this item is super shit. It's gonna give you 80 damage without reductions only when your target has 2000 hp, and that's not likely to happen before 25 minutes unless he builds hp on purpose, and if he does, then why the hell are you focusing him? Long story short, build this first, deal 0 damage, lose the game for your team. No, this is not good even on Kog'MawSquare Kog'Maw as a first item. He already has % damage. I'm skeptical about this working late game as well, because if your opponent has high hp, he probably has high magic resist as well, so you can increase your damage and dps against him more cheaply by grabbing Last Whisper item Last Whisper. TL;DR: If you bought this as a first item, remember that time you got kicked in the nuts? You diserved it.
How to understand what your carry needs.

Even though carries basically have similar builds, as in every carry by end game will probably have The Bloodthirster item The Bloodthirster, Infinity Edge item Infinity Edge, The Black Cleaver item The Black Cleaver/Last Whisper item Last Whisper, and you will try to get Boots of Speed item Boots of Speed as a starting item or on your first return, the build order is extremely dependent on the AD carry that you're playing.

I will clear things up on what makes carries different: Range. Natural steroids may also be considered, but they don't make that much of a difference in this. Range is the most important.

So, probably by this time you either know exactly what i mean, or you're wondering what the fuck i'm talking about, but I'll treat you all equally and explain.

AD carries are auto attack dependant. The damage they deal is depending on it, and range dictates how far you can be from your target while still being able to do your damage, ergo your overall safety in team fights/harassing/last hitting in a lane. This separates carries into two build categories: Short range carries, and Long range carries, and they hold the answer to the question "Do I build BT first, or do i build IE?".
Short ranged carries:

Because of their short auto attack range, These carries become exposed to alot of harassment during laning, and will usually get damaged if they try to harass or duel. Basically, the short range makes them take damage no matter what their positioning is, and this is a crucial problem in dominating your lane and securing farm, as well as surviving battles.

Examples of these carries: Sivir, Corki, Ezreal, Vayne, Graves, Miss Fortune.

This influences the first item you should rush: The Bloodthirster item The Bloodthirster. You need damage. This doesn't change, remember this. However, you also need lifesteal to survive. This is normally the best damage item that you should rush as a short range carry. It's fast, and it's fun, and I'm gonna stop picking on hotshot now.

So you secured your safe farming tool and can now proceed to become a late game god while also being able to breathe easy. What we care about now is also giving you some dps. Somewhere around this time, you should work towards Berserker's Greaves item Berserker's Greaves and Zeal item Zeal. This combo provides you with enough AS to have decent dps, and also the speed to be relatively safe. The crits will also help you. Now you basically have covered strengthening your dps, and you don't have to visit the base every 3 seconds, so NOW you can finally build Infinity Edge item Infinity Edge. Finish PD, and now you have a properly built ranged carry. From here on out, It's a matter of you being flexible more than anything, so what follows are just pointers that you need to look out for.
Long range carries:

I'm gonna start by saying these count Ashe, Tristana, Caitlyn, Kog'Maw and... These are the only ones that fit here.

Now, what's important on these guys is that their range allows you to rush Infinity Edge since they are usually very safe, and that's exactly what you're going to do. Acquire it as fast as possible, then get Phantom Dancer. What you're doing right now is called abusing the shit out of your range. Theoretically, these champs give you enough range so that you can harras and farm, as well as pound the shit out of anyone safely, so not abusing the shit out of the fast IE PD combo with the range you got, you're basically commiting a crime against the League.
Stuff that matters on both.

You're gonna need an item that allows your damage to pass through, because duh, armor counters you. The choice goes between The Black Cleaver item The Black Cleaver or the Last Whisper item Last Whisper. How to pick? More than 2 targets have <160 armor and you have a full armor pen rune set, get TBC. Otherwise take LW. You HAVE to take one of them, this isn't a choice, even if you're absolutely stomping. TBC removes armor so it will make targets you focus get stomped THAT MUCH FASTER.

Second thing you absolutely need is a TANKY SHIT. This tanky shit ammounts to an item that makes sure that the enemy can't enlarge your butthole in 2 seconds if you're hit by CC. There are different alternatives to this, but mostly this item is all about magic resist.

- Wit&#039;s End item Wit's End: This really sexy item is a great dps item disguised as survivability. You're getting 50 MR along with 50% AS and 42 damage? Count me in! Warning: This item is to be taken only if your team can do a good job in keeping the enemies off of you. If your team is full of retards whose priority is chasing kills, you shouldn't. You should instead get:

- Guardian Angel item Guardian Angel: A really underrated item for carries, and I don't know why. 100% pick when your support is soraka because once you revive she can burst heal you. This item does not only make you very solid because of the great armor bonus and decent mresist bonus, but it will drop alot of aggro from you, since the enemy know that if they focus you first, you just spring back to life. Also great for keeping your BT stacks

- Banshee&#039;s Veil item Banshee's Veil: The enemy has a moderate cooldown CC spell, this is the item for you. It also provides good mr, and best of all, hp and mana pools. A choice item for almost every AD when faced with a strong burster.

- Quicksilver Sash item Quicksilver Sash: This is more underrated than GA, but extremely good as well. You get a huge mr value, and most importantly the remove all debuffs active! Get this each time your enemy has a game breaking CC such as Galio or Amumu's Ult, Rammus's and Fiddlesticks's 3 second single target CC. This way you won't die every team fight while doing nothing
Up, up, down down, left, right, left, right, B, A

Like the title suggests, these are builds that allow you to cheat your way to a fast Infinity Edge even if you have a short range whitout being harassed into oblivion and feeding a whole cemetary with your deaths:

You have two basic options:

Option 1) 3 Doran&#039;s Blade item Doran's Blades, B. F. Sword item B. F. Sword, Zeal and then finish Infinity}}. 3 Blades provide you with the respectable ammount of 30 damage, 9%lifesteal, which along with the mastery makes as much as a vamp scepter, and 300 extra health which is a nice health pool Theoretically, this should be able to save you if you have a bad lane phase

Option 2) Wriggle&#039;s Lantern item Wriggle's Lantern, BF Sword, Zeal, Infinity Edge. Wriggle's is a solution for the advanced player, and note that you shouldn't go on this build path if you started with Doran's Blade, because it will delay your infinity too much. This is a solution if you started with boots, Cloth Armor item Cloth Armor + 5 potions (My honest opinion is that you shouldn't start with Vampiric Scepter item Vampiric Scepter or Long Sword item Long Sword). Let's take a look at what it provides for 1600 gold: 30 Armor: very good in mitigating the harassment you get from the enemy AD; 23 AD: self explanatory; 15% lifesteal: this, along with the armor, should make you pretty much invulnerable to harass. So far, everything's straightforward. Let's get to the advanced tactics wriggle's allows you to do: 20% chance to deal 425 magic damage; this offers 2 things that you can absolutely abuse: counterjungling; you can do small invasions in the enemy jungle to steal camps and ram your jet up the enemy jungler's arse. If your own jungler does his own part in the top jungle, the enemy jungler can kiss this game goodbye; second thing is faster buff and epic monster clear times. With the proc, you can finish baron, dragon, and/or buffs really fast, which means more safety and reliability in these cases. And the best thing is free ward every 3 minutes on a 3 minute duration. THIS IS AWESOME, SON. Faceplant this bitch in the tribush or at dragon, and you can farm in safety even if your support ran out of wards or suffers from "I'm stupid and you can buy your own wards cuz that's not my job" syndrome (i got this in ranked, it's real), OR ward your enemy jungler's bottom buff, and go steal dat shit whenever it's up, though i recommend playing a carry with a wall jump ability like Ezreal or Graves to do this one, so that you don't get caught and the jungler gets the buff with you on top. These things will make up for the fact that you're paying slightly more than for 3 dorans, along with the fact that it sells for 70% of it's price, while doran's will sell for only 45% of their price.

Mother of TL;DR

If your carry is short ranged, get bloodthirster first, zeal, then infinity edge, finish with phantom dancer.

If he's long range (range >600), you can go directly to the infinity edge plus phantom dancer combo.

If you're short range but stil want to rush Infinity, build either 3 dorans or wriggle's, a bf sword and a zeal before finishing infinity.

Whatever you do, you're gonna need to fill two slots with a penetration item, which is gonna be The Black Cleaver or Last whisper, depending if your opponent has less than 160 armor or not, and the other will be a survivability item, which is gonna be wit's end / guardian angel / banshee's veil/ Quicksilver sash.

Always build damage first, and zeal + berserker greaves are enough attack speed and crit for early game.

Hopefully this guide has enlightened you on how to build items on ranged AD, or not, let me know in the comment section. Constructive feedback regarding my writing style is also welcome.