PROS

+ Good Early engage
+ Tanky
+ Brings good point and click CC
+ Good in team fights
+ Amazing against auto-attacking champions
+ Can fish
+ "Who wants a piece of the champ?"

CONS

- Child predator jokes

Surprisingly, Jax has a decently strong engage as soon as he reaches level 2. With a point in your E and Q, you can go for a quick trade on the enemy ADC that will push them back and maybe even burn a spell. Besides this, you are just farming till you get level 6, since that is when you become a proper tanky.

After you have your Ult, you have the advantage in battles, since your Ult combined with the Aftershock runes make you incredibly tanky early on. Pick fights when you're able to and just harass the enemy lane. You're also able to turret dive any low health enemy. I would suggest either flashing in with your E, or using Q with your E, stunning the enemy and either you or your ADC getting the kill. Afterwards, use flash to get out, or use Q on a minion or your ADC to get out.

Mid game, you should always stick with your ADC. Jax support cannot get kills alone, as your entire purpose is to tank and stun. You take towers somewhat fast thanks to your W with spellblade on Trinity Force, so try to push in any lane you can with a teammate.

Late game is a feast or famine type deal. You either are really good, or suck booty cheeks. Since most of the fights late game are team fights, your Ult really pops off, since the amount of resistances you gain stack with the amount of enemies hit within your Ult. Your E is also a fantastic tool during Team fights, since you want to be using Q to jump on the entire enemy team, popping R, and stunning them all with your E. As with Mid game, you never want to be alone. You are a team player, and only a team player. So long as your with someone, you can easily catch out any lone enemies and kill them with your stun and follow up from a teammate.