Hey, I'm Aatrox Bot and play on EUW (currently Run DMP). This guide is how I got from bronze to silver in season 4 (not overly impressive) and how i got from silver to gold in season 5. I had started maining Aatrox in mid season 3 however i started playing ranked a lot more in season 4 in which i played just over 150 Aatrox games and had just over a 62% win rate.
Now i am going to teach you how to play him. This guide will be updated often hopefully and please comment so I can work on the feedback.

If you are against someone strong early you can start either Dorans Shield and pot or long sword and 3, this will give you enough sustain early to be able to farm after you use your pots you may want to try and freeze the lane by your tower and sustain with your w. If you can you should only use pots above half hp because below 50% hp your w does 3x the heal. If you are against a low damage melee champ like a tank then start Dorans blade and pot, it will give you a nice bit of ad lifesteal and health which lets you do a bit of damage and sustain easier.

Your Core build is simple, as a fighter you want to do damage as well as take damage. With core stats being AD, lifesteal and AS. That being said your core build is Bortk, Randuins and Spirit Visage. The Bortk gives All 3 of your main stats needless to say that this is a good item also giving a great passive of 8% hp on hit this combined with the mass amounts of AS from your passive and ult makes it almost the only damage item you need. The randuins is a great allround tank item, armour, hp, an AS slow for the enemies and a movement slow. Lastly the Spirit Visage is great for a tanky mr item and with the passive being amazing for Aatrox, 20% increased self healing which will apply to your W and Passive so your bloodwell will increase the health you revive with by 20%!

Due to your high sustain the laning phase becomes alot easier for you, a resourceless (well you use health) champion can almost stay in lane forever but never let this fool you, if your opponent has backed and bought then you will be at a large advantage so try and go back when they do or when you hit a good amount of gold to buy an item. Farming can be very easy on Aatrox, all you have to do is take the poke from your enemies while killing minions, your w will heal you and thus canceling out the enemy poke, if however you find yourself taking too much damage then you can sit back and farm with your e and try to hit low health minons as well as the enemy champ. if you are planning on pushing your lane be sure to have your passive and ward the river for ganks.

You can use your ult for taking towers, never hoard it for fighting as the cooldown is low enough.
Put you w on damage whilst above 50% hp then switch to heal below that as your heal is much more efficient this way.
If you find youself ganking bot lane early with tp you can get the first drag solo too due to how easy it is for you to do.
If your finding that you are losing lane always save your q for escaping.