The best option you have playing Jax on the Top lane is to chicken at your turret and miss farm, otherwise you feed too much till level 6.
At level 6 you still chicken at your turret against some opponents because they are just too noobish AKA Riven (no hate, 110k on her).
After you have got sheen just hit the minions twice then activate your W and hit them right in the face and then hug your turret till you are ready for the slap again. If you don't deal enough damage to make them p#ssy around then better stay safe. You are THE lategame beast anyway.

Try to use teleport to use drakes and win teamfights. You can also use it to to split hard and then teleport into a teamfight.

Roaming is always worth. You can pick up a kill or bait some summoners for probably 10 farm, when you roam at the right time. Lets calculate. If you lose 10 and get a kill for that, it is very simple: 10*20=200 vs 300+150=400. You get twice the gold you wouldve gotten on your lane. If you dont pick up the kill and you bait a summoner the jungler can gank easier to pick up the kill, so it is worth in anyway to roam, aswell because you will lose lots of farm anyway when you have to stay under the turret if you aren't a good farmer.
The roaming itself is very simple. You walk onto the lane behind them and E -> Q them for the cheaky stun. The harder thing is to know when you have the opportunity to roam. I would roam, when you have pushed the lane and your opponent begins to freeze. Then he will be busy freezing and probably won't even notice that you are already fed.

You are Jax, that means you got teleport and can push a lane while your team will try to fight them at drake. When the fight begins you watch it, while pushing and when you see a good chance to teleport in then show them the Power of Jax!
Power of Jax:
You just jump through their frontline and dominate their backline instant with a stun in the face of the ADC or APC. After that is done you kill the rest: Pentakill
That sounds quite easy (what it is), but their is still a kind of art behind it to get the right moment engaging. And you should better not forget to press your ultimate before full engaging right into the backline, otherwise you get bursted. You should try to take down the ADC fist, while your E is activated, so you don't take damage at all