This guide was based on Maknoons build for Jayce in the semi-finals of the 2012 world championships.
Basicly this build is orientated on maximizing damage output on early levels, using shock blast trough acceleration gate as strong distance poke, and To the skies into Thundering blow combo when needed.
The early armour penetration from the brutalizer synchronizes very well with this strategy.
Maxing Acceleration gate fast will also allow you to escape early ganks more easily!

Notice that we immediately max shock blast and accelaration gate in stead of putting points in Transform. Since hyper field doesnt really do that much dmg on early levels, we leave this skill for last. If you find yourself getting out of mana quickly you can put one point in this skill early on.

Since Jayce is a highly skillcapped champion, dealing most of his dmg trough his abilities and not by auto attacks, we end the build with Infinity edge and Last Whisper maximizing total attack dmg. (Note that Hyper charge gives max attack speed for 3 attacks, undependant of total attack speed, meaning that this skill scales heavily with total attack dmg)

Pro's:

-Best long range poke in the game.
-A decent amount of crowd control
-Can inflict insane dmg to health stacking tanks (Thundering blow deals % of Max Health)
-Can be played as Bruiser and AD carry, depending on build and skill order.
-Built in Shurelya's Reverie
-Excellent farmer
-Spammable ult that gives you a speed boost to get back in lane just that little bit faster :p
-7 abilities -> Extremely fun to play

Con's:

-Needs some items to do dmg
-Not good vs early aggression (eg Kennen, Olaf, Yorick, ...)
-More of a late game champion (although this build tries to fix that!)

Lots of people may ask: why not max your ultimate whenever you can, and why no points in Lightning Field / Hyper Charge?

Well here's why:

One point in R grants: - +10 armour and magic resist when in hammer stance
- +40 damage after each transform to hammer stance
- +5% magic res and armour reduction for 5 sec in cannon stance
Where as
One point in To the Skies/Shock Blast grants:
- +(55x1.4) = 77 damage per shock blast
- +45 damage per to the skies
-> Much Much Much More Damage :p