This build is really designed more for myself as I work on learning how to play Jayce. I'm not really sure about the runes build. I don't own any and if anyone bothers to read this guide I wouldn't want to misguide them. Follow a different guide for the runes. I used other guides to give me an idea of what might work, but i don't have the runes to test it.
Like I said this build is for me, but I will go on to explain my reasoning for those who want it. Any advice is welcome, this is my first time making a build. I've looked to other builds for ideas. The last build just wasn't good enough. It worked fine till late game where it had trouble against beginner bots, so I had to scrap it and start new. Anyway here we go.

Heads up: If you're going to use this build, use item sequence 2. So far it seems to work best in most situations. Build 1 still needs a lot of work. Build 2 is for durability, while I'm trying in build 1 to get a better balance of durability and damage.

(By the way the title is a reference to Dr.Horrible's Sing Along Blog. Look it up. It's good.)

Jayce's attacks primarily focus on Attack Damage (AD) so I chose to focus on the left half of the attack masteries section. The Summoner's Wrath in particular, I wanted to mention, was chosen for a couple reasons.
1.) Ignite. When used ignite gives the champion 5 Ability Power (AP). It's almost insignificant, but it improves the damage dealt by lightning field.
2.) Exhaust. This reduces the target's magic resist and armor by 10.

Addressing the defense section. Jayce, like most champions, has naturally higher armor than magic resist, so in the masteries I put 3 in Magic Resist and only 2 in armor so I'd still have a point for the 30 extra health.

I choose to max out Q first because to start the match it's his only move that deals significant damage while playing safe early on.
The next move I chose to max out was his E skill. In Hammer Stance the E skill -at level 5- deals 20% of the enemy's max health (plus whatever it's base damage is and what comes from your AD). In Cannon Stance, this skill sets up the acceleration gate. The Acceleration Gate can be used to propel Shock Blast at faster speeds, or it can be used to help yourself and allies flee the battle scene. Together I felt this skill was more important than the W.
Lastly I chose W to be the final skill I max out. While it's useful in both stances, I felt this one just didn't quite match up to the 20% damage dealt by E in Hammer Stance. In Hammer Stance it sets up an electric field that deals magic damage, so it doesn't scale with your AD and deals low damage regardless of your AD. In Cannon Stance it sets your Attack Speed to maximum and causes your auto attacks to deal bonus Damage. The problem is from a distance on a character with lower than normal range it was easy for champions to step just outside of range causing you to have to chase them down, so it becomes next to useless sometimes (a bit more on how to use this skill differently later).

I know you want to learn to play, but I'm not a teacher, nor would I consider myself amazing enough at the game to teach. There's no fun in getting all the info from a guide. Go make a custom match and learn the skills. There's no better teacher than practice. It also helps to watch ranked matches to learn a few combos you may not have thought of.

A full combo, anyway, in case I get rusty: Hammer Q + W (in the air) follow up with E, then to cannon E + Q and finish with W.

Honestly, I'm not too sure which build is which since it's changed a lot recently, and I've been testing quite a bit. Build 1 is currently my main build, works well so far, and is currently under testing.
build 2 is essentially the top rated olaf build atm because I want to give it a try and see what it does for Jayce. See which items work, which don't, and i'll work from there