Jax is a very special champion that can neutralize almost any champion depending on your build and your skills. Some important tricks to play Jax are very simple:
1) If you have Flash and you want to kill your enemy but he is out of range to your Q then, tarjet him with Q then Flash, or Q + E + Flash.
2) You can jump with your Q to Wards and allies, that means you can steel Dragon if you are Jungle. Placing it near to the Dragons place walls.
3) Some combos I personally use:
A)Q + W + E + R
B)Q + E + W
C)E + W + Q
D)R + W + E
4) I personally forget to activate R many times I should but, I am so fed that I do not need it; literally. This build is like an extra R.

Jax can be one of the best teamfighters of the game, specially by his passive. E is the most important of his habilities, specially to push/carry out any lane. If you dominate Jax´s habilities than don´t stress on your habilities too much, concentrate that Thunderlord´s strike him up every time you attack, so someone else get the kill, if you are low life or out of range gg. I particulary use Flash and Ignite on Top Lane, when I Jungle just Smite and Flash. If you play Jungle Jax never ever choose Ignite as a spell... I´d played vrs. other Jaxs that have Ignite and they are Jungle and I wreckt them out easily, obviusly in early game the other Jax will have some kind of advantage but, then it will have many disadvantages. AD and AP Jax suck alot vrs. this build in my opinion, if you try it out you will know why I say this. This build isn´t for noobs just people who have good masteries and runes. High Elo...

Pros
1) Amazing late game
2) Devourer will make everything easier
3) Common to get a first blood if you invade enemies´ Jungle/Common to get first blood on Top Lane by Ignite easily and silly how fast you can combo somebody in Top Lane
4) Ganks against you aren´t to effective (Put wards every time you can near you, so you Q when you see that the enemy Jungle comes in the Gank)
Cons
1) If you ran from any Marksman Champion then you´re wreckt (Specially Kalista)
2) Not getting kills means your build will wait longer to get completed
3) Corrupting Potion get useless after building Guinsoo´s Rageblade
4) Ganking aggresivly causes huge waste of passive