Try this guide out on 3v3. I've had great success with this, keeping positive K/D even when I lose.

Dodge seals are necessary. AP glyphs are good, I have 3 magic resist / lvl glyphs since I can't afford all AP and it gives survivability. Magic Pen, Armor pen, and Attack speed marks are all good. I am using armor pen quints now, since I had those, and no one else uses dodge quints.

Ninja tabis and rageblade every game and hextech gunblade every game. Sheen is useful to make your leap/empower combo more deadly. Rageblade makes you dominate teamfights. Hextech Gunblade gives you a way to finish people off who are running away with its active, and gives you a lot more survivability and makes it so you don't need to recall for health, just go jungling instead.
Starting off I buy one or two health pots. Next I buy ninja tabi's, and either sheen or vampiric scepter. Then start rageblade, maybe buy the 300 gold armor if I need it, and finish the build.
Hexdrinker is helpful if you're going up against all casters. Thornmail if all melee DPS, but even then I hardly ever need it, since I can already dodge so much. Otherwise stick with the build.

The important part is lvl q,w,e then q a lot so you can reduce the cooldown to be in line with w, and level the ult whenever you can like normal. Look at the cooldowns and try to keep your q and w at the same time, and level q before w, since you can use it for chasing or running away. Don't forget to leap away towards a friendly minion if you are outgunned.

I use exhaust and ghost. It's good to have one offensive and one defensive spell. Ghost is normally defensive, but I get quite a few kills with it too. Others to try are exhaust and cleanse.
I have also had success playing offensively (w/ offensive masteries) with exhaust and ignite.

Last hit minions like normal, and if you push to far, go jungling. Coming in with q,w and press e to stun you can farm well at low level. Lizard buff is very helpful for Jax, as well as AS buff when you get guinsoo rageblade to get it ramped up fast.

At the beginning you are low health, so try to play the assassin. Use empower leap to harass before committing to a 1v1 battle. At the beginning you have to be careful with mana, but after getting sheen, I don't have to worry about it anymore. Take the top lane if your partners let you. It really helps to have a tank on your team, since jax is squishy until very late. It doesn't matter as much whether the 3rd partner is magic or damage, since this Jax does a lot of people already.