Pros

REALLY BIG Damage Dealer
Naturally Tanky
Easy 1 vs 1 Champ
Easy farming Champ

Cons

Only 1 sec cc
Hard get closer

First of all dont think that youre Damage is the highest in game
instead of better try to get the most last hits if the enemy champin comes to near to you so give him an autoattack and then use your empower to maximal Damage dont chase him the Minions could stop you or prevent that your harrasment was that effectively.
If you know that u can kill him then do it but better think twice before just killing him.
My super advice to you is Jax may be one of the strongest champ in league but never forget WARDS and pls u dont need them only for the escape also to avoid DANGER and to KEEP OBJETIVES SAVE placing wards is not only the work of supports.

Good early Game

For Example your early game was REALLY GOOD u are the strongest at the moment dont think about teamfights keep pushing top lane until someone is coming to help the enemys top lane after that u can decide whether u keep pushing top further or go safe by farming other lanes chilling in the jungle and wait for tf.
Or you can help your bot lane by ganking them kill their adc kill their squishy jungler kill the ap carry or do dragon whatever help your team.

Bad early Game

If u had a really bad early game u got so destroyed you wanna leave NEVER think that u are useless try to get Blade of the ruined King after this item u should be able to kill the enemy adc; buy Tryforce GET ALL MINIONS at the Map bring yourself back to the game U WILL BE ABLE TO

At this moment NO ONE CAN ONE VS ONE U srsly i tested it i played against a Nasus which had 1100 stacks on his q I killed him.
So keep this in mind.
At the late game you should just kill their adc which is faster then killing the ap carries like Fizz Ahri Gragas mostly because they HAVE a ZHONYAS after AD Carry and AP Carry are Dead go for the squishy one maybe the support maybe a Riven or a Rengar just go further and kill all after you got youre "e" ready.

Mostly guys are talking something like Jax is such an OP BEAST and yes he is but dont think he is a easy champ like Teemo what u need for Jax is Experience I just saw only One Jax back in season 3 beginning where he bought all jungler Items and he Killed everyone.
Why ?
Cause he didnt waited for some 2 vs 1 he just go throug the minions and killed one go to top kill the other one what I want to say is Jax is a BEAST which reqiures a lot of experience dont think he is too overpowered.

If you readed this whole piece of whatever Guide (I am German and my English is like u read XD)
I want to wish you good luck
and thank you if u would play like I guided u