PASSIVE:Relentless Assault
Jax gains Attack speed 3.5% − 11% (based on level) bonus attack speed for 2.5 seconds every time he lands a basic attack, stacking up to 8 times for a maximum of 28% − 88% (based on level) bonus attack speed. Stacks fall off one at a time every 0.25 seconds after not attacking for 2.5 seconds.
Your passive gives you more attack speed every 3 levels it upgrades at levels 4,7,10,13,16. Before reaching one of these levels you should stack up your passive on minions and when you level up you can start a fight with your opponent.
This passive makes Jax one of the best splitpushers in the game.
Q:Leap Strike
Jax leaps towards a target. If it's an enemy, he attacks, dealing 65 / 105 / 145 / 185 / 225 (+60% of ability power) (+1.0 per bonus attack damage) physical damage.
You can use it to jump to wards, plants, minions, monsters and champions.
It can be empowered by your W.
W:Empower
Jax's next basic attack or Leap Strike Leap Strike within 10 seconds deals bonus magic damage. If Empower is used on a basic attack, it will have 50 bonus range.
Empower resets your autoattack and gives it bonus range.
It won't deal bonus damage to tower but it will proc your Sheen.
E:Counter Strike
Jax enters Evasion, a defensive stance, for up to 2 seconds, causing all basic attacks against him to miss. Jax also takes 25% reduced damage from all champion area of effect abilities. After 1 second, Jax can reactivate to end it immediately.
At the end of the duration, Jax stuns all nearby enemies for 1 second and deals physical damage to them, increased by 20% for each attack dodged, up to a 100% increase.
Don't engage without it and remember the cooldown.
Perfect for level 1 fights because you will dodge minion damage and deal more to enemy.
It also dodges auto attack based abilities like Gankplanks Q or Ezreals Q.
R:Grandmaster's Might
PASSIVE: Jax deals bonus magic damage on every third basic attack within 2.5 seconds of each other.
ACTIVE - THE CHAMP: Jax gains bonus armor and bonus magic resistance for 8 seconds.
Use your Q to get close to the enemy use auto attack then reset it with W and with Hydra, this fast three auto attack combo procs your ultimate's passive and later in the game is enough to kill a squishy target.
Use your ultimate to reduce burst damage from enemies.

Before we start try all the runes listed below and find out which are the best for your playstyle.
Conqueror is you main rune it gives you ad true damage and healing. But if you want you can take Grasp of the Undying, Hail of Blades or Press the Attack for better early game I even tried Aftershock against some champions but most of the time you will use Conqueror.
For your main rune path we will stick with Precision.
Your first rune is Triumph. It helps you snowball and survive fights.
For your second rune most of the time you take Tenacity but if enemy team doesn't have CC you can take Alacrity or Bloodlone.
Your last rune in Precision is either Last Stand or Coup De Grace it's your choice.
For your secondary runes you have few choices.
In domination tree you can pick Ravenous Hunter for some healing from your abilities and Taste of Blood for more sustain in lane or you can take Sudden Impact for more damage after your Q or Teleport.
In Sorcery tree you can take Nullifying Orb against ap toplaners, Nimbus Cloak to get out from bad situations or chase people, Transcendence for cooldown and ad or Gathering Storm for more ad late game.
In Resolve you can take Demolish for better split pushing and you can chose between Bone Plating against burst damage or Second Wind against poke.
In Inspiration tree you can take Time Warp Tonic and Biscuit Delivery for better survival in lane, Magical Footwear for free boots and bonus movement speed or Cosmic Insight for more cooldown reduction.
In Shards first you take attack speed second adaptive power and third armor or magic resistance.

Trinity Force is your big power spike and core item that gives you everything you need.
Spear of Shojin is your second power spike and with those two items Jax can fight anyone.
Most champions change their trinket later in the game but on Jax you need your Warding Totem for ward jumping.
Hydra helps you proc your ults passive and gives you wave clear.
High health anti burst item with shield and tenacity plus ad.
It synergize with hydra (more health=more damage) and it makes chasing people easier.
Penetration item buy it when enemy team has at least two tanks.
If enemy team has healing or life steal and you need ad defense buy Thornmail.
Anti crit item with aoe slow armor and health good vs fed adc.
If you don't need armor but you need anti heal and penetration buy this.
Very good item it gives you armor, ad and revive.
Good item if your team has healer or you took Legend Bloodline.
Good item against mages with damage over time or spammable abilities.
Buy it only against champs with very hard cc like Malzahars R.
Good item it gives you magic resistance life steal movement speed and you can reach attack speed cap with this, Trinity Force, Jax's passive at level 16 at 8 stacks, attack speed shard and Spear of Shojin buff.