Hi, i'm a mastery 7 Jayce player on two accounts totaling over 300k total mastery points, and this is my guide for him. Ive been using Jayce ever since I was level 13 which was last year, and he has always been the most fun champ to play. You get to play with 6 different abilities, and they deal a lot of damage and give tons of speed. The builds are in order from left to right for what you should get. Good luck in battle.

PROS:
6 Abilities
Carries
High Mobility
Deletes Towers/Champs
Great Ganker
Snipes
Great Poke

CONS:
Mana Hungry
Skill Shots
Squishy
Requires Some Skill
Gets Focused A Lot

Jayce has an AMAZING poke advantage. Use your Q+E combo to get the enemies down to low health before you decide to team fight, this allows your team to win all fights!
When your team decides to go all in, Q the enemy ADC while in Hammer Mode, AA them, E them and they will die.
When your team is running away from the enemy due to a loss team fight, place your E (While in Cannon mode) so your team can run quickly away. You can also place your Q through your gate once you pass through it if you have the time.
While Laning, your enemy mid laner will always stay in mid lane with half health or less for some reason. Keep an eye out for when that happens, Q+E them and you'll get a kill everytime. If not, then they'll be a one shot, and back, which helps your mid laner farm more/gank bot.

Jayce has probably the second greatest wave clear.

Level 1-6

Your attack speed runes help you a lot with killing multiple minions.

level 7+

Your Q+E combo on your Cannon mode will kill all minions hit. His Q ability on his Hammer stance mode knocks all minions to death or to one shots.

Make sure when you're farming early game that you keep 3 ranged minions alive. Tank their damage at the peak of your tower, to where your tower cant hit them. Doing this freezes lane, and allows you to farm easily. It also allows for easy ganks top for your jungler.

This is the current history of my Jayce games right now. If you're using Jayce, he is great for destroying towers. Going for the objective is much better than trying to get the most kills on the team, wish these recent games showed the towers I taken (Pretty much all of them every game). Always split push with Jayce, he has an amazing wave clear and can 100-0 towers before an enemy can even get there. If an enemy happens to be right nearby though, you can still manage to get out of there using your E (Cannon mode) + Youmuus + R combo.

(Some of the matches were done in Normals due to my internet being slow, I will be posting more ranked history soon)

Thanks for viewing my build, have fun with it. If you have any questions let me know.