Best way to farm is with mercury cannon. First level try a bit harass enemy with range, if he try harass you, you can use your mercury hammer E ability, it deals alot damage and knocks him back. Then you reach level 2, laern Q ability. After level 2 you can terrorize your opponent with melee hammer, just use on him Q and E, and run away and farm with range cannon. Do this again and again until he hug a tower. If he wont hug a tower, it means you can kill him, again same combo with hammer, if need use your ignite, if this not enough and need much more damage you can also use your cannon E+Q combo(if you laern this combo, first bood always goes to you).

Always ward river/bush. Jayce pretty strong in mid game. Your E ability is max level, now you almost unbeatable, just dont do stupid moves and everything gonna be okay. Harass enemy, gank mid lane, gank enemy jungler (you can gank with jayce enemy jungle alone, jayce have great escape ablity's. if u gonna be in trouble just use your E and run away.) Help mates take drake, always go in team fights, dont stay in your lane too long.

Here is the problem, jayce not so trong in late game, but if you play right (in team fight always try kill enemy's most dangerous champions) you can carry the game.

Malphite is the only one counter against jayce (played against all top lane champions, i lost only against malphite.). Against malphite i reccomend play passive, just wait your jungler ganks. That harass with Q+E combo is too risky, cause if you get closer near malphite, he can do his combo and u will loose alot hp and farm.
Play against irelia is pretty hard, but do that Q+E combo and irelia will hug a tower and everything gonna be okay.
Renekton- dont fight against him till u reach level 5, he's way too strong for jayce in early game.
Riven- good riven can beat Jayce pretty easy if riven is pretty agressive. If you play against agressive riven, better watch out, wait untill your jungler comes to gank. Against passive Riven just do that q+e combo and she will hug a tower.
Pantheon- Jayce can beat pantheon pretty easy, no matter how aggresive pantheon is, u still can beat him in early/mid/late game.
Jax- In early game jax a bit too strong, so better get a bit magic resist and armor. And harass him with Q+E combo.
Rumble/vladimir/teemo/kayle- worst champions against jayce are ranged champs. So easy kill them, just harass them as much as you can, dont give a farm and dont push a lane, 100% win in top lane.

I hope this guild gonna be useful.

P.S. Sorry for my english :]