I've always considered Jax to be my secret weapon. Everytime that i want to win I just pick this champ. So, i decided to share my build with you, which has brought me very happiness :D

I usually use Magic Penetration marks and the rest Ability Power. Why? It gives you a great boost early game and also helps late-game of course.

I go with defensive masteries for survival and of course, the dodge mastery which is amazing for jax because it gives you a speed boost everytime you dodge, and you dodge a lot. I also get Sorcery and Archaic Knowledge in Offense because of the CD and the magic penetration, since Jax is AP based.

Why 3 Hextech Gunblades you ask? For 3 obvious reasons:
1. Gives you a great boost in auto attack because of the attack damage;
2. Gives you a great boost in skills, because it gives you a lot of Ability Power;
3. And the main reason is because it makes you almost unkillable, since you have 60% Lifesteal and 75% Spell Vamp after building the 3 Hextech Gunblades. And it adds you lots of HP from the passive.

Guinsoo's is obvious, because it gives attack damage, ability power and the passive stacks with your ultimate.

The Rabadons is almost unneeded since i only got to it one time or another. It's for really really late game, when you still haven't won and you want to, buy the Rabadons. I killed a teemo with about 2000 hp with just Empowered Leap Strike and the stun. With this item build i can enter an unfair fight and still win with half hp or more, if i am smart.

Your skill sequence is simple. Press W for Empower and just Leap Strike the enemy. If you don't Empower your Leap Strike, it will deal less damage. After you're in the battle, always press E for stun. Counter-strike ( the stun ) is the main reason why jax is so good. Even if you're against a stronger champion, the stun can turn the fight to your side, and grant you a victory. Just stun stun stun... and stun a little more. And another thing: Jax is awesome for chasing. Why? Because you can literally jump on your enemy, dealling a lot of damage and catching up to him.
Relentless Assault. You just gotta love this skill. It's great for farming, with enough ability power, your third attack deals tons of damage and it's every caster's nightmare, because it gives your magic resist based on your dodge percent, which is about 28% end game.

So, for people who don't like to read a lot: W -> Q -> E.
If against casters: R -> W -> Q -> E.

I consider Jax to be a great tower diver. He can easily finish a champion off just by using Empowered Leap Strike and igniting the enemy. I've already done this even on low lvls, like 2 and 3.

My favorite summoner spells are Exhaust and Ignite or Ghost and Flash. The first two help in battles, the other two help running or chasing.

Farming is essencial as your item build is very expensive. But if you play good enough, you can get tons of money from frags and build your items easily.

This is how I play Jax, and it's really rare to loose. I'll play some games with Jax to show you my scores so that you can see the true Power of Jax, the Grandmaster at Arms.