Jayce is a lane bully. Nothing else.
False!
Let me prove it with this build!
Jayce is strong in early, mid AND lategame.
Plus: play him kinda offtank and he's not even squishy.

Jayce isn't really hard to play.
The best that can happen to you is that you're on your lane before your enemie gets there and you get ahead in levels. Against most champions you just got to poke til your enemie is on maybe 40-60% HP and then you can easily kill him with being one Level ahead. Just be sure that your enemie hasn't got too much infight sustain (much lifesteal like lee sin, or a great heal) Because the enemies minions could kill you before you kill the enemie.
If you and your enemie are pretty even there is only one way to win: POKE. That is what jayce is there for. Poking like ****. And it's easy, especially against meelees. You will soon be able to kill your enemie with your great burst damage (which you've got double, Cannon Stance and Hammer Stance)
If you are behind (which happens often against people like Xin Zhao or when the enemie jungler is camping top) Build Sustain and HP. The dmg you'll be needing comes per level anyway. As soon as the enemie is gone roaming, push hard and take down the enemie turret with Hyper charge.
The lane should be won then.

This is just one small tip:
If your team is invading, hide in a brush in hammer stance. If the first enemie comes and facechecks your brush, DO NOT use your Q on him directly. Wait til he turns and trys to run, then take advantage of your gapclosing "To The Skys" and it's slow. It's gonna be first blood for your team for sure, even against tanks with ~800HP on level 1 (check out my Shen guide).

Four letters:

ROAM

you are fast enough to run to midlane with your ulti to gank succesfuly and you've got tp to go to bot, or back to top. If you feel there is a turret that needs some pushing, do it! with Hyper Charge and the extra damage on you're first hammer stance AA it'll be down in secs.

Pros:
-Damage Damage Damage
-High mobility
-Pushing and Splitpushing is easy
-High burst damage
-excellent Poke
-easy to get ahead with
-brutal comeback in midgame if behind in early
-looks cool

Cons:
-Squishy in early
-Very vulnerable to ganks in the first few levels
-May get snowballed now and then due to squishieness
-Needs much mana (take advantage of this disadvantage and build Muramana and it's cool)

Very easy with jayce. It's no problem really, just farm in cannon stance so that you won't get harrassed by your enemie.

Try to hit their main carry with a Accelaration Gate and Shock Blast combo if possible, then change to hammer stance and jump onto him. Use AAs til your ult is up and then finish him of with hypercharge at the latest. But keep in mind that while doing so you might be killed, so stay in safe positions where you can disengage again easily to not get killed by the enemie team. Their carry alone shouldn't be a match for you tho. Jayce is OP against squishies.

Just Roam. I said it before and i'll say it again. Pushing is what you can do best. Killing comes right after. Use this to make your team's lanes winning lanes.
Try to place your Accelaration Gate so that your team can take advantage of it.

If you want to play Jayce jungle, no problem. I can give a few tips for that too:
When you gank best jump out of a brush with To The Skys and slow the enemie like that. Knock him into the direction of your teammembers if possible. If you're ganking bot, the adc should be down in seconds. If he gapcloses away tho, use your accelaration gate to Shock Blast and chase him do death finally with Hyper Charge.

Jayce can be built offtank or full ad and is strong enough either way.
If you want to be succesful with jayce just roam.
Be cautious in the first few levels.