This is a guide to play Jax if u want to become OVERPOWER. I am not a mega pro but i often win when i play like this.

I have attack speed and dodge. attack speed gives u a huge advantage in low lvl, and dodge give u nice dodge percent and u will easily take first blood if u use your exhaust.

I take 21/9/0 like many others do with Jax. That can save u in many situations.

Doran's shield gives u hp and some armor. very good starting item.

ninja tabi is a must. it not only gives u speed boost, it also gives u dodge and armor. which is very good.

hextech gunblade is an amazing item. it gives u damage, ability power, life steal, spell vamp and gives u a ability to slow and deal massive damage to a target. i think it's a must for jax.

sheen is very good, it double your basic dmg after you made an ability. i like to buy it after hextech when you have like 170 dmg. then with your sheen you do like 340 dmg!

guinsoo's rageblad gives u dmg, ability power and attack speed with every hit. very good item for jax.

bloodthirster give massive dmg and life steal. when you bloodthirster id fullstacked you will have +100 dmg and 25% life steal. very nice item for jax.

and last the trinity force. it gives you everything and a passive bonus that make you next basic attack dmg 150% more dmg after used an ability. u will crush you enemys.