Welcome to this EXTREMELY OP build of my fav champion Aatrox, you'll have full Crit. and lifesteal on those Crits so constant health regeneration.

You can alter attack damage for attack speed but I haven't tried it out yet as I do not have the runes nor the IP for it. Armor gives you some extra tankiness and the CDR is just essential.

This is set aids very well your life steal as well as giving the extra survivability early game... Feel free to change to your preference.

Start with basic Doran's and a Health potion, use only when health is below half with no minions around.
Wait for 900 gold and return to get the scepter, it helps a lot and gives you great LS.
Complete the build for Bloodthirster and use any gold for Guinsoo's. It should be easier this time as you get into fights and gain gold much faster.
Procede with Essence Reaver as it gives good CDR and AD, Shiv gives a good AS and much better Crit. chance.
By now you should be shredding enemies so go for Infinity Edge for extra Crit. damage then complete the Crit. Chance with the Phantom dancer.
Note you can go for them both at the same time, i.e. you can buy Cloak of Agility for IE and Zeal for PD.
This is the final build, if you find yourself dying a lot change Guinsoo's for Hextech Gunblade, for extra damage use Guinsoo's. Aatrox's Q provides mobility so boots aren't as necessary.

Max your E first, it scales very well with AD and AP, go for W next as you'll need the extra damage when active, Q comes at last as the benefit of the other skills outweigh that of Q.

Cons: No Blood Well, no kills, more deaths.
Q can be stopped so make sure to time it correctly.
Stuns are crazy potent on Aatrox so try to avoid them.
Pros: At full Blood Well and Guinsoo's stacks you attack speed is crazy fast.
Crits damage go up to 1500 and heal gives you about 30 % of that so health is always there.
Easy one shot ADC's.
Fast recharging skills as with Crit Cooldown provided by Essence Reaver you get around 37 % cooldown which is simply awesome!!
He's Aatrox guys, that's a pro :D

You'll find difficulty to some extent at first against ranged champions as they attack from range (duhh!) Use your E then to keep the pressure and keep them at bay.
You'll find yourself a great initiator in team fights and you can easily 1 vs 1 champions.
Make sure to grab a Yasuo or Amumu as allies as your knockup will give time for Yasuo Ult and extra time for you to attack. Amumu 's Ult also keeps enemies in place for the real Massacre to occur!