So about the build..
I think this is the most balanced build for jax for now (preseason 6) after the botrk changes its better to not get it since there are more valuable options, yes you lose sustain but you still have tankiness and the sustain from Maw. If things dont change to the start of season 6, jax's build will mostly look something like this(toplane jax).So i havent seen many jaxes top, so far only jungle but i still think that jax is insane if played well and this is the build for toplane, just w/o botrk.

Not gonna go deep into the guide since its my first one and league is such a complicated game, way too much things to talk about and many situations but this is early game basics.

You are starting with E which means you can trade at level one really easy because of the reliability of basic attacks to all the champs but against something like vlad or swain, things might not work out since they will just run and wait for your e to end.Then you get Q and you can use it to escape or as a gap closer remember to use your wards to jump on them if there are no minions when you get ganked while out of position.Just dont try too hard to push the lane, lane push is complicated and its hard to explain when to push or not.
After level 6 you can trade with ranged champions much easier just hit twice on minions jump on enemy hit aa with ult passive then refresh aa with w, and this is the basic trade after 6

Remember to tp at good positions and help your team and if you lose your lane do the same and just try your best to farm and dont die

Mid game is pretty much farming/taking objectives like towers and dragons sometimes early barons just help your team and farm as much as you can.

Remember that dragon no longer gives gold so its not fatal if you lose 2 or 3 drakes, you need to be sure you know when to contest drake since you can lose the fight and give away gold + dragon

Take advantages of enemy bad positionings, since you can really easy take out squishies like ap and ad carries.Tanks arent problem aswell with this build but you need to prioritize carries

Thats pretty much the basics of jax with this nice build.Of course this is like 10% of the gameplay explanation but as i told you its a really complicated story, you need to improve by playing, watching streams/guides and just explore deeply into the game in order to understand it and be skillful with the mechanics.