Jax is one of those champions that everyone thinks that jax was so op and anyone could play him but they were wrong... I have seen several people that have thought that since, they saw jax be so op and awesome that they could just look up a build and go rape with him. They were wrong, it takes time, skill, game habbits, and experience to do well as jax in most games. ( granted the ocasional easy game where the other team is a joke) but to all you fellow jax players I hope this build helps you out.

Hes just a different champion because he can play so many roles in game.

I stick with Attack Damage Marks, Ability power glyphs and quints because I think that it the most useful throughout the game but especially late game because it just gives you that little extra edge from the start so you should be ahead a little bit xP

I put my masteries in mainly offense but i like to put some into defense because the extra armor and dodge chance is really nice to have. I dont put any into crit because i feel that jax doesn't need crit to do well in games.

I pick clense because you never know when your going to get those games where there are so many cc on the other team you just want to cry because you know that is going to be one tough game.

I usually go with the ninja tabi but if there is more than one cc (which there usually is in every game) on the other team then I go with merc treads because it really helps in teamfights and survival.
For the ending item (BloodThirster) i normally go with when the other team is very balanced because of the extra life steal on top of the gunblade and the bonus stacks help if you farm a couple waves. You may also go with:
rabadons (if the other team has a ton of armor or you just need a little more hp).
Banshee's Veil (if their team is really balanced and you need that extra hp and mana along with the 30 sec spell shield) xP
[phantom dancer/sword of the divine if you want the little extra attk speed
or just your own ending item if you seem another ending item fit (it is just your own judgement due to what you seem fits best).

At the begining of your game play with jax I usually just try to sit back behind the minions, and get as many cs as i can but not losing too much hp you can grab 2 and a mana pot if you wish i choose to save my money and try to get through this expensive build as quick as possible.
Mid game with jax I try to either sit and my lane as farm as much as i possible can, but if the team needs ganks and no one is taking the chances on your team then you should help them out and then gank as much as you can scooping up some cs at the same time after clearing the wave you just fought in.
Late game... this is were you become god xP once your have 3 or 4 final items you can see a huge difference in jax's ability to own. This is were the other team hates you and always tries to focus you in team fights... hence the clense and merc treads. And you can basically go into any fight and feel confident. This is where you are starting to decide your ending item. As to the item list above, use accordingly and the game should be over... or just makes you more invincible, and easier to finish the game when ever you want... hehe
Thanks for reading my guide i hope you liked it and leave some feedback for what i did wrong and what i did well. I would like to get better at writing builds so i am able to keep going at it in the future.