Laning phase
You should always get level 1 E and if enemy champion gets in meele range autoattack him and block his auto with your e and you automatticly won trade, don't fight when the enemy laner has a huge minon wave you will proc Conqrueror and you will win that trade almost every time only if you aren't against jayce or some ranged matchups which can kite you when you don't have q. Level 2 you get your q and if they are lower hp than you jump on them and try to trade or even get the first blood or their summs. Level 6 you have good kill pressure because of your ult passive and also ult gives you mr and armor so you are a lot tankier. Be careful on ganks always ward and don't waste your e and q because then they can gank you.

In most situations you want to splitpush botlane and bring tp with you so you can tp in fights where you can win and get objectives. Jax is a great splitpusher because of his passive and w, everytime turn on w on turrets so you will destroy them faster.
You can also use tiamat for aa reset but when you have a lot of attack speed you won't even need that.

+Excellent duelist
+ Can fight almost anyone late game
+ Extremely strong late game
+ Great splitpusher
+ Has a built-in escape with ward + Q
+ Has an auto-attack reset
+ Gets naturally tanky in fights when using R as it gives you a good amount of resists

- Can be shut down with CC
- Hard to get back in the game if behind
- Requires matchup knowledge
- Has some difficult matchups
- Can sometimes struggle with teamfights

Trinity force
Maybe the most important item for Jax. It gives Jax everything he can want. It has nice boost on his attack speed, some damage, movement speed, but most importantly it gives him the Sheen proc that makes Jax deal so much damage in short bursts.

Titanic Hydra
This item is extremely efficient when looking at it's stats. It gives Jax HP which is always good especially early on, some damage and most importantly it improves Jax's wave clear immensively.

Hextech Gunblade
This item gives lots of healing and some nice burst to kill squishies aswell as let you live longer in fights since it heals you for 15% of all damage you deal.

Blade of the Ruined King
This item has been bad for quite a while, but it recently got buffed to 12% of current health for melee users (as physical damage) which might make it viable for some games since it makes dealing with juggernauts and tanks who have a lot of HP much easier. Armor will still deny value from this item but champions like Sett might not always have a lot of armor so this might be a good option into champions like him.

Thank you for your support i hope this guide was helpful for you.