Not Updated For Current Season
Jax is the jumping chainsaw. His attacks can absolutely rip through anyone, and with this build you manage to slice through your opponents armor, and magic resist. This build is primarily AP, because of the fact that malady provides MR reduction, and AP.
A.Pen Marks - Cuts the edge off of a hero's stock armor.
Dodge Seals - Self explanatory, Jax's survival = Dodge.
M.Pen Gylphs = Cuts the edge off a hero's stock MR.
AP Quints - Because you want a leg up on the AP side of this build.
I prefer to use empower first. Its your lowest cost skill, and its damage output works well for ganks. You can chose to put it into counter strike, but it depends then on who you are facing, and if you are targeted first.
I max Counter-Strike first, and then empower, and then leapstrike. Leapstrike is your initiator, its not meant to be used as a constant attack.
Ghost is a fantastic get away for jax, as he relys on dodge. If you manage to encounter an AP hero, its worth it to invest in this so you can escape.
Alternative : Exhaust
Ignite is very helpful in taking down tanks, and for throwing on someone who is low enough to die from it, and you dont want to turret dive. It makes a great finisher, and you can use it as well to finish off someone, and change targets.
I dont recommend replacing this with jax, because the build gives you a tickle more AP when its on CD, which is helpful early-on.
Helping other lanes:
Come up behind the gank, and attack them head on. Keep your Q ready for persuing them, it helps to recover from a stun, or when they ghost and are low HP.
Try and attack the creep wave first, and get your E up. Then W,Q,E, and then follow them with ghost. Do not pay much attention to creeps when you are ganking. Your high dodge lets you tank creeps through a gank.
After Jax has his Rageblade, he can solo dragon, or anything else for that matter very easily. Try and snag a few creep kills inbetween down times in the lane, jax will tear through jungle mobs, and make it back to the lane in record time.
Try and follow up with a gank, keep in mind jax's Q works over walls, it is good to try and take advantage of this, and take your enemy by surprise.