Jax, is a very powerful champion, if played with kind of AP/AD build.
This build represents my playing style of Jax

You can also use this build to jungle because Jax fits for everything!!!

Runes focus to attack damage and ability power.
I won't talk about them more than that.

Masteries focus on low cooldowns and low summoner ability cooldowns.
In offence, focusing on to AP and bit to minion damage.

Items go as well to regular AP/AD build.
Ninja Tabi is a good item because you really need dodge chance to stun with "Counter Strike"
Hextech Gunblade is a must have item. It gives AP and AD and also Spell vamp and Life steal.
Guinsoo's Rageblade is a good item because it stacks and every stack gives AP and attack speed.
With these you can easily clear a minion wave by just Auto-Attacking.
Bloodthirster gives you bit more AD and lifesteal.
Rabadon's Deathcap gives you tons of AP so you can maximise the damage you do with "Leap Strike" and "Counter Attack"
Last item is Infinity Edge which gives quite a lot of AD and crit. chance it also makes your crit. damage hit 250% of your regular AD

Leap Strike is very powerful in early game, and if you buy AP you can really do damage in late game too so max it quick.

Empower gives your attacks more damage you can max this last.

Counter Strike is powerful because it has a stun but it needs a dodge to activate.

Relentless Assault (Ultimate) on activate you will take reduced damage.
But it's passive, stack (10 times). Every stack gives you more attack speed. Also every third attack makes additional bonus damage.

Ghost: Really good summoner spell for escaping.
Also you can get quite quickly to your destination if in hurry.

Ingnite: In masteries you have point in Burning Embers. It grants you 10 AP while ignite is on cooldown.

If you want you can also play this build on Katarina because she is also good AP/AD champion.
But still, never underestimmate your opponents. Its important to know if you can or can't kill someone (except in teamfights). So go to the Fields of Justice and kick everyones *** with "Jax, Grandmaster at Arms"