Aatrox is an auto attack oriented top lane AD bruiser. He is squishier than the likes of Renekton or Shen, but deals much more damage. He is like a tankier Tryndamere with hard CC and more sustain.

The runes I take are pretty standard. 6 flat AD reds to help in early trades, along with armor pen. once they build some armor to counter you. The armor to stop most top laners, as they are usually AD, and scaling MR to lessen that late game damage from AP Carries. The Flat AD Quints will also give you more general early game power.

I take a point in Summoner's Wrath for that extra 5 AD when ignite is on cooldown. 5 AD early game makes a big difference in trades. 4 points in attack speed, as Aatrox is basic attack oriented. 1 point in Butcher to make CSing easier. Next are standard AD masteries along with Destruction in order to do even more damage to turrets than I already do, thus increasing my late-game backdoor potential.

I build BotRK as a key item, as it gives life-steal, attack speed, and attack damage, all of which Aatrox can utilize to the fullest. It also gives chasing potential. Blood-Thirster is also a core item because it gives more AD and life-steal which Aatrox uses well. I was deciding between Hydra and BT, but I decided to get BT so that I can dive in and do more damage to the squishies. The Black Cleaver is also core because it gives us AD, armor penetration, and a bit of tankiness.

I max W first in order to max out the sustain/damage I can do in trades. Next, I max out E so that I can poke my opponent. My Q is maxed last, as it is used mostly to move around or to knock up enemies. Of course, I level my R whenever I can.

I take flash because it can be used in so many different ways. And I take ignite for the extra damage that I can do with it, and to start snowballing after securing a kill in lane.

After laning, Aatrox is also a huge threat in teamfights. If you can land your Q and knock up as many people as you can, and use your ult to damage as many people around you. Then proceed to start chopping away at the enemy carries.

Poke with your E.
Pop ult when feeling like trading.
Fight when your passive is full.
Don't be afraid to go man-mode and all in because your passive will help a lot in a dive.
Toggle your W until you reach half-health, then turn it off. You will heal a lot more when your health is below 50%.

Since you are a basic attacker, it is pretty simple to farm. But in order to sustain, you must get 3 hits off which in turn does push your lane. This is the weakness of Aatrox. Trying to get 3 hits off pushes lane making you an easy target for the enemy jungler.

Pros:
+Amazing Sustain
+Gap Closer
+Good Poke
+Basically a tankier Tryndamere
+Decent through out the game

Cons:
-Hard to land knock up
-Hard to land poke
-Not very good until first buy or so
-Slightly squishy
-Sustaining with W tends to push your lane