What do I do in teamfights as jax?

Target the enemy carry who is the greatest threat, jump on them, bash them in the head. E + HP and magic resistance should make you tough to melt.

What did you build?

Pop ult, jump on the ADC/APC

Build kind of tanky. Ult and try to hit a multiple stun for engage. Don't try and fight the whole team by yourself make sure you on the same page with your team to combo your CC and clean up the fight. I have at many times jumped into the team and got shredded because my team wasn't all on the same page. Time your engages properly. It takes some bad games to learn from your mistakes and I have had many bad games with Jax.

Look up some rune and masteries builds too. You never go wrong with a great build. It will boost your gameplay even if you are not great mechanically.

after you have triforce and bilgewater cutlass, you can pretty much build straight tank on Jax, and finish the BorK later. Your Ult also gives a bunch of resistances when active, so that should help you out.