Hey I'm Rustle, and I decided to make a build guide for Jayce. He is a strong hero that when fed can easily dominate the region with his attack speed and damage output. Using his abilities from the hammer and bow form help you to achieve victory. This build was inspired from HotStevo69's build, they are very similar and most of the credit goes to him, check out his build; All Hail King Jayce and give it an upvote.

I believe playing mid you need these two spells to sustain and dominate.
TELEPORT
Teleport is important as you need to out-farm the opposing midlaner early game, the ideal setup is to have two people farm mid on the opposite team (yes, very unlikely but the goal). This will help you to achieve higher levels and give you more opportunities to grab some kills from their greediness. As you will gain gold you need to sustain this xp lead on the enemy mid-laner, teleport allows you to quickly go to the shop and comeback without missing out on too much farm.

FLASH
I believe every build should have flash. Flash allows you to surprise and escape from enemy attacks, the worst thing to do in League is to die, giving the enemy a lot of xp and money, an advantage. Flash allows you to dodge their attacks and save yourself. Flash also allows you to jump over walls, surprising low-health enemies or junglers.

GHOST
A lot of builds recommend this spell, I honestly thing it is a waste of time and space, the movement speed won't allow you to truly stay on another champion's heels unlike flash. Also Jayce's 'E' ability is basically a free ghost spell with a shorter cool down.

EARLY GAME
Early mid-lane game you need to have you're 'Q' key unlocked first, this will allow you to consistently poke the enemy mid-laner, forcing them to have to recall for health.

HOW TO GANK OR KILL STRONGER OPPONENTS
GANKING
In order to start ganking you NEED your 'Q' and 'E' abilities unlocked, if you didn't know if you shoot your 'Q' ability through the gate made from 'E' you give 40% more damage to enemies. The way you should gank is to wait for enemy player to push much past you so you are nearly directly behind them, you put your 'E' down and then shoot them with your 'Q' this will give them a fat load of damage and surprise them activate your 'W' for that attack speed and hit em hard, if they manage to escape either quickly run through your speed gate (created from 'E') and chase them OR press 'R' and turn your weapon into a melee hammer, then free 'Q' to dive onto them and finish em off.
KILLING STRONGER OPPONENTS
Before you engage with a tanky opponent you will need to poke them a bit with your 'Q' ability constantly sending out strikes. after they are under a health that you think is decently small then follow the same steps in the ganking phase. If it is early game many tanks champions will try to take you on when low, rush back to your tower and use the 'E', 'Q' combo and they will take fat loads of damage and you'll most likely end up with some gold in return!

END GAME
With most of your items completed you become a carrying monster, if you engage combat with your 'E' and 'Q' combo then smack them with a 'W' you will most likely kill them in seconds with the attack speed and damage you will be putting out.

ROAMING
I prefer to roam and gank with my weapon in the ranged format, this allows me to quickly use the 'E', 'Q' combo and annihilate my opponent. This also allows me to put down my speed gate ('E') if I run into someone a bit stronger than myself making my escape easy and usually saving my flash for something else.

Item guideline
Ranaan's Hurricane
This items helps you to clear waves on minions with ease! The ability makes it so you're primary ranged attacks shoots two projectiles instead of one, with all the crit-chance and attack speed you can solo minion hordes!

Infinity Edge
This blade will help you to deal immense amounts of damage with few attacks. The high crit-chance and attack speed will help you to determine the outcome of the match.

Death's Dance
You're a mid-laner, you need to be a sustainable champion, Death's Dance helps you to take damage overtime and gives you enough life steal to survive from ganks adn hard pushes from the opposition. This is why you need to rush this item early, playing with lower health you need to make sure you're never vulnerable.

Thanks for looking at my Jayce guide, this is my first build guide and any tips are appreciated. Please up vote this build and feel free to test it out.

Thanks - Rustle :]