Passive: Relentless Assault
This is what makes Jax the potent duelist everybody knows of. Makes you win prolonged trades automatically activating using your AA and W in rapid sucession is a 20% Attack speed gain in about a second.
Q: Leap Strike
I max this second, Decent damage but with a high mana cost. You can jump to allies/wards/enemys just about everything that is targetable. This scales pretty well with AD so its more practical to max W instead because it has a high base damage with a low cost and resets your auto attack
Your Bread and Butter,Nachos and Cheese,Tea and Crumpets or whatever you call it skill. This can outright win you trades, proc your passive,Proc sheen it is just an all around amazing skill to have maxed first. With a mana cost that is lower than q it is quite spammable in lane.
Note:Almost always use right after an auto attack to build your passive up and your ult passive up.
E: Counter Strike
100% dodge for 2 seconds! What is not to like about this skill. It provides CC and durability. This is what makes you the hard counter to AoE damage dealers like Karthus or Anivia and Auto Attackers like Irelia or Rengar. It also has deceptive early game damage that many people unless they play Jax don't understand.
Note: Activate after dealing damage with AA or W then the attacks from minions will boost your damage up and also not to mention will result in your mitigating a lot of minion hostility.
R: Grandmaster's Might
The passive on this ultimate deal a large sum of magic damage on each 3rd attack making Jax have insane burst for knocking enemies off their feet.The activation is no slouch either making Jax into an insta tank. Jax is usually an attractive target in team fights since it relieves Tons of damage and pressure. By activating this you turn this choice into a difficult one since he will be very tanky. Just remember not to pop this until you take damage since it kinda makes it pointless to use it before they even choose to attack you. As with any ultimate max it 6,11 and 16
Note:The passive of this ability can be manipulated by attacking 2 creeps then the opposing champion for some quick burst.
Also i didnt include a skill order chapter since i think i explained in pretty good right here.