Your first item should be cloth armor and 5 pots. this should be followed by vamp septer and dodging boots. Try to get a hexblade followed by a rageblade. Then get another hexblade before getting a trinity force. finish the build with yet another hexblade. It may seem redundant but jax gains mad amount of hp with this build. Even if the other team has a character with a bloodrazor, you can easily kill them with your lifesteal. If you are worried about characters with high damage output like tryndamere or master yi, dont worry, cus your stun will own them. a well timed stun wont even let trynd ult against you. as for high ap characters, you should hav enough hp to eat whatever they throw at you and then afterwards, you can kill them. Next to this, your masteries allow you to take a beating even though you are NOT a tank. Without a doubt, there is no other character that will win a 1 v 1 against this build due to the tanky hp, high ad dmg, high ap dmg, stun, and reduced damage due to your masteries and dodge.

Dodge runes are a must for this character because of his counter-attack ability.

I like to have ap and ad runes to give even more hp and dmg output. I also like to have armor pen and magic pen runes for some of the tankier characters.

Generally i get the same items shown above because they generally always work. If you somehow run across a team of all high hp characters you may want to substitute one of the hexblades for a razorblade, but i prefer the build i have above. It is literally unstoppable in a 1 v 1 situation.

I get the magic pen in the offense for some extra dmg output and max out the defense not only for the extra dodge chance, but also for reduced damage and extra ap power/attack speed.

Jax is slow to start up, so i generally like to att minions to get his att speed up before a fight.

Jax's stun in conjunction with Leap Strike is great for stopping pursuers or chasing.

I know most other guides say that jax should NEVER initiate a fight but believe me you can. If you get your counter-strike ability up, and their team is bunched up, use empower followed by a well placed leap strike and finish by stunning their team with counter-strike. At this point it would be a good idea to pop your ult followed by using your hexblade on one of your enemies. Be completely sure that your team will back you up!... there is no point in initiating if they wont help you so be coordinated... in a premade team mics can be good for this.

I like flash to get out of tight situations or to catch fleeing enemies.
I use exhaust for the same reason, but i also use it to take out their best ad dmg output so that i can be more helpful in team fights.

Other viable spells are ignite, ghost, cleanse and teleport.

Pros
High AD dmg output
High AP dmg output
High HP
has a stun
very easy to use in late game situations (especially when you solo baron)
Cons
slow to start up in fight
conditional stun
only has 1 ability that does area dmg so limited in team fights