Hi!
I play a lot of Jax (otherwise I would not be making this build)
My success has come from a lot practice and understanding of how everything works.
I'll stop rambling and build.

Pro's
-Freaking BRILLIANT if you can hold out to that late early game stage
-High Burst at lvl 3
-Even though frowned upon by 'Pros", Can mid
-Can drop health like Dubstep
-Split Pushes harder than anything

Con's
-CANNOT Initiate
-Will be focused after you start bursting (or earlier)
-Can 1v1 or 1v2 fine, but needs help from the team in most cases (no being the hero all the time)
-EXTREMELY vulnerable to blinding

RUNE'S
Just really quick on these.
Jax's auto attack is one of the things to be FEARED late early game to end game. I take attack speed and damage just to give it a little shove. I find also that defense on Jax helps a lot in any part of the game. On quints, I love the movement speed so I can close the gap for the jump, but evasion is not a bad choice either.

MASTERY'S
9/20/1
I want the evasion and move speed bonus from it, reduced cool downs and magic pen, and one last point in ghost for that brilliant chase or escape.

So I take mid as Jax as much as I can, but I can't all the time. This should work in both lane and this should work for both.

Early game
At lvl 2, you can get EMPOWER (w) and this leads to a lot of early game harassment. If you activate EMPOWER, it will add damage to your LEAP STRIKE instead of your auto attack.
If you get your E up, Do as follow

W, Q to target, E and run away.

Slowly depleting anyone's health. On mid its a bit easier to get aggro, and easier to get your stun up quicker..

Late game

The Rage blade is your best friend. After being bought, your auto attack can drop towers like no body's business. When the moment is right, split push. Your team thanks you.

Jax isn't really THAT hard to play, but if any of this confuses you, leave a comment

This is my first build:P Working on how to use MOBA fire, bear with me, it'll get prettier! (and fuller =_=)