Not Updated For Current Season
This is a custom Jax build that I adapted from a couple of great guides
Note: Sell Dorans ring at about mid game. Also if your going up against more than one tank in either 3v3 or 5v5 I suggest getting The Black Cleaver right after the Trinity force and drop the Malady at the end.
I will update this more as I play but since I've started using it I haven't had less than a 3:1 ratio for kills:deaths. Theses are the items I choose, and usually if I'm soloing a lane I will typically buy 1 or 2 health potions too. But otherwise as I have time I will add some tips on what to do with Jax early, mid, and late game along with some of my experiences against specific champions. My first guide will be quite obvious but its against a champion I'm sure most of find quite annoying unless you are playing as her; Evelyn.
In order to win a match against a team that has an Evelyn you must MUST buy vision wards and place them around your lane (they last 3 minutes each), and suggest to your teammates to buy them as well. They will detect her when she goes invisible and tries to sneak up behind you. Also I would suggest mid game and late game when you have about 400 extra gold, like that ever happens :p , but if you do buy Oracles Elixer, it will allow you to detect invisible champions around you and allow you to not take that initial hit from Evelyn as she comes out of her invisibility spell which does some serious damage. The key to fighting her is to not allow her to build up a kill streak, even if you have to target her you need to suppress her early game and keep her down because once she gets most of the typical items Evelyn uses, its pretty much game over at the end. One thing I've found that works against her as Jax is to use your Empower+Leap Strike when shes still invisible (detect her from Oracles Elixer) this will do enough damage to her before she can hit you to allow you to solo her every time, otherwise you will want to use your Exhaust spell against her and get some help if she gets you too low a health. Obviously all of these tips are champion independent, if someone is using an attack speed build as Evelyn, which she should, then you will need to adapt and always have one or two other teammates with you to take her down mid to late game.
Well thats all for now, like I said as I play more I will put more tips on here. Good luck everyone!