Hello. I'm a silver player(sadly) on EUW server. My account name is aPillowWithCorn and I started playing more Jax recently. In this guide I will tell you some tips and things I like to do which may or may not work in higher elos. Enjoy.

Do you like insane lategame?
Do you like feeding and still 1v1 their carry with 3 items?
Do you like to tilt enemy adc's?
If at least one answer is yes, than Jax is for you.

Fervor is hands down the best keystone on Jax right now. Provides better early trades and really good damage overall. And since Jax is an auto attack heavy champion fervor is a realy good choice. I saw some people playing with colossus but I don't recommend it.

Triniti Force with gunblade are the only two damage items you need. Although I usually put rageblade in too, it's not necessary. I like to build Triforce into gunblade into Randuin's into rageblade into visage. This is just my order but I highly recommend building either triforce or gunblade first and second. You can also just not build rageblade and get GA or zzrot or mallet or maybe even titanic.

Cons
Weaker early game
Reliant on hitting E (in most trades)
Pros
Late game carry
Can literally three-shot
Almost impossible to 1v1

As Jax you give yourself a much easier time in teamfights when you build two tank items. This allows you to jump in and escape or kill some people. You should focus on stunning as many people as you can and then killing the most important ones like adc or whoever is fed. Because of your lifesteal and tanky items and your ultimate you have very good sustain and can tank a lot. If you don't hit your E well retreat and wait for it to come back up.

In lane try to trade a lot or deny the nemy of cs because even if you are ahead you can easily 1v2 or even 1v2. Jax doesn't really have any hard matchups so that is also very good. Try to trade with your empowered Q then E stun then auto and empower auto to probably even kill someone lvl 3. As jax you can also be very aggressive so sometimes if enemy jungler starts top you can E and trade so the enemy toplaner can't give a leash or else you'll kill him when he gets back to lane.

As I mentioned before, Jax is a really strong lategame carry/splitpusher and can solo carry games like no one else. He has a lot of outplay potential and can 1v2 even when a littlebit ahead. You have insane split push, can 1v1 squishies aswell as tanks and has a decent laning phase overall. You can build almost anything on Jax and it will work so feel free to experiment and figure out what the best build is for you. Good luck!