Aatrox The Everlasting!
This is going to be relatively short, As this is should Be taken as just a backbone to build onto how you play,
This is a guide on How to play Aatrox And have an impact.
I recommend you try this in Coop vs AI before a PvP so you can get used to it.
This is just what I find to work the best, If you find better feel free to change to preference

With this skill Seq. You should be able to do fairly well at farming Early game because his E (the starting choice) is OP and has decent range, decent damage, and Slows. Plus it cuts through multiple targets without losing damage as it goes through each one like some champions. That with the fact that Aatrox Heals after every third hit (I do not like to toggle until late game or at full health, Even then it makes Aatrox harder to play as every third hit will damage you) makes Aatrox very good at staying in his lane and Farming.

Aatrox Combo!
Q,R, Auto Attack (until they run, Which they will because your Ult has Static damage/Increases attack speed), E, Whatever Number your BotRK Is (Blade of the ruined king for those who don't know), And Q again. Make sure to Use your exhaust if they still are not dead (They should be)

Aatrox has by far one of the BEST Passives in the game as he comes back to life, And the enemy can do nothing but watch.
You Fill power this passive by using His abilities.
This is very useful if you need to chase and end up dying by a turret on your way back.

These Items through Trial and Error have been what I have found best. I am not 100% sure if spirit visage helps with Aatroxs W or not, But with the other items it makes 1v1 against nearly anyone a breeze. Attack speed is important with Aatrox because the more hits he lands, The more health he recovers which means the longer he can fight and force the Enemy champion to fall back. Then using the combo I mention above you should win every fight.

Aatrox is a fairly decent Jungler due to his passive to gain health back, However In my opinion Aatrox belongs in the top lane, Not the jungle. I normally only go into the jungle to basically heal myself Late game by attacking The forest minions or to Get the red buff.

Aatrox is a farming beast.
His Q does area damage, His E slices through Multiple minions, And his W recovers His health.(Unless you Toggle it which I really never do)

Pros:

Aatrox is pretty much unbeatable in a 1v1

Can Easily stay in lane for a long amount of time

Pretty good range with Q and E

The Ult has amazing Range and Static Damage

Cons:

Can die rather Quickly in a team battle if not played smart

After Aatrox is revived by his Passive, He is easy to be killed.