I am not going to tell you my own stats to attempt to lure all of you to my guide. Instead I will tell you that this is one possible build that I have had success with in my time playing League and if you would like to try it, I bet it will bring you some success as well. That being said, enjoy...

Runes and Masteries make a big difference in your success but I cannot attest to one set up being the best for me and for the sake of different players having different levels, rp, and ip, I will not include these in my guide.

Depending on your team different summoner spells may benefit you better than heal and flash; however, (special cases aside) heal will be great for last stands in lane and along with flash, will allow you to make clean escapes. Personally I enjoy having teleport to allow me to recall, buy items, and get back to defend my turret quickly. Both spells have their pros and cons so pick your favorite.

This is a crucial point to your starting game and ultimately will be a determining factor in whether or not you will win your lane. Assuming you have a descent idea of what your are doing and you are last hitting minions, you should at least have 760+ gold before you recall. At this point you should buy a long sword and a ruby crystal for AD and health as well as two or three health and mana potions depending on what you can afford. Now if you really know what you are doing and you can farm well and maybe get a kill or two, you can easily have 2150+ gold and you can skip straight to buying a vampiric scepter and a Phage as well as health and, more importantly, mana potions. Either way that is what ultimately what you want to rush.

Boots, The Bloodthirster, and Trinity Force are a strong, well rounded core build that you will want to get as fast as you can. Trinity force will help improve attack speed, health, mana, AP, and AD while the bloodthirster will give Jax the damage he needs to really push lanes and kill champions, as well as a much needed boost in life steal.

The first piece of the final build you want to buy is an Infinity Edge, heavily boosting his AD and critical-strike chance. This can be followed with a zephyr which provides a great boost in attack speed as well as another boost in attack damage while reducing effects of stuns, slows, and all other immobilizers. Another option for attack speed is Wit's End which could be more useful against a heavy AP team. Your final item should be Frozen Mallet. Once you buy this, it will be nearly impossible for any enemy to escape you while you deliver deathly blows at insane speeds. When your health is low, one wave of minions will revive you to full health in seconds. At this final build, Jax can solo Baron while losing very minimal health.

The rest is up to you. A build will only get you so far in any match, the most important factor is how you play, how well you understand ability combinations and how to play offensively or defensively as needed. Anyway, try this if you are looking for a good build, it really won't disappoint you.