Aatrox is an amazing melee ADC. He has High sustain and a great kit to cc any attempted escapees. With built in boosts to attack speed and damage he is nasty 1v1, and with his passive stands a good chance even in 2v1 situations. The rest of this guide will explain the items and his style of play. One word of warning, because of his blood well "revive" it is very easy to get a feeling of invincibility with him. As fun as it is, that will get you killed if you aren't careful.

This is a pretty standard top set up. I never see the use in scaling runes on top lane champs. The effect of Runes diminishes over the game where the items you buy make a greater impact. Attack speed is Paramount to him using his blood price/blood thirst to the greatest extent. Attack damage should be pretty self explanatory for an ADC.

I Rush for Warmogs, he is very well set at every stage of the game, and getting that 1000 health early gives him greater sustain. Boots are helpful in keeping him in combat and not letting his blood well dry up, and running if things don't go so well. After Warmogs its sort of a toss up between Bloodthirster and Phantom Dancer, he has enough attack damage that he can go straight to speed. However, the Lifesteal is imperative to keeping letting him use Blood Price without consequence. After that, I get the Ultimate Crit chance items, Infinity edge. Once I've gotten this far into the game, a critical hit on his Blood Price hit will do 700+ damage to minions or dragon. It's safe to say you don't *need* more damage and could build tankier, but since when has need stopped us? :D
Ravenous Hydra and Black Cleaver would destroy anyone. However, Spirit Visage and Randuins Omen would make you a hard opponent to focus out of team fights, where Massacre will mop the floor with them.

Blood Price/Blood Thirst is Aatrox's life blood, literally, Blood price builds up his blood well. and Blood Thirst heals him every third hit, I strongly recommend this as your first maxed ability. On the plus side it costs nothing to switch the toggle. then I'd get his Dark Flight, the ability to knock up crowded champs is such a great teamfight saver. Obviously his ult takes precedence over everything and the last to max is his reverse cone. it slows but the cost outways it's benefits early on