This will be a short guide since it's my first. But i do hope it will help.
Basicly this guide is about building Jax to make him really good. I will also tell you tips on how to use him. Runes and masteries will ofcourse be available. Making the build requires gold so farming minions is a MUST. Go alone if you can but don't riske your life. I don't suggest jungling as Jax, he is better on the battle field.

When you look at the skill sequence, you will se that first unlock Leaping Strike. At level two you unlock Counter Strike. Use these two skills together. First activate Counter strike, then use Leaping Strike on your target causing damage and making you take less damage from normal attacks. Once Counter Strike fades out it will put all targets around you into a "Sleep Mode" Meaning they will be unable to perfom any kind of actions. Once you've learn Empower combine Empower with Leaping strike to cause more damage with it (Only do that if Counter Strike is on cooldown or an enemy has low health). At level six you learn Grandmasters Might. Activating it will make each third strike cause additional damge. So when attacking an enemy/enemies do the following: Counter Strike + Leaping Strike. Empower. Grandmasters Might. Remeber that Jax is NOT a tank, even though his high health would make him look like a tank. Always let your teammates attack first, making the enemy focusing on them instead of you. When they do that it's your turn. Use what i've told you and take down they're health. But beware! Use Empower carefuly if there are ranged champions around, ranged has easy to get kill steals. But if you spare your Empower and wait untill the enemy is at low health you can take him/her out without thinking of the ranged. And as with all champions, a kill for a death isn't neccasary. It's killed or be killed, but don't let them kill you once you've killed them! I suggest switching alot between the lanes when playing Summoner's rift, helping your whole team. Since Jax can do insane damage he should go top lane, because the towers at the top lane has the most health.

When playing as Jax, use Exhaust and Flash for both fleeing and getting closer to enemies. Both spells can be used as an escaping tactic and a killing tactic. Exhasut= Slow down your enemy. Flash= Teleport a small distance in any direction.