-- TIPS --

Poke with ACCELERATION GATE and SHOCK BLAST as often as possible, but TO THE SKIES! and THUNDERING BLOW (and LIGHTNING FIELD if you can spare the mana) are great poke too, especially if done immediately after your SHOCK BLAST + AC GATE poke, as you close the gap fast and immediately disengage (Just make sure you don't THUNDERING BLOW and disengage when they are low health).

When poking in mid-lane before team fights, never fire your SHOCK BLAST straight down the middle, stand to the side of the lane and fire parallel down the lane, or aim a little towards the center of the lame. And as mana shouldn't be an issue, don't be hesitant to shoot into the fog, as your range is mental.

DO NOT use THUNDERING BLOW lightly. Using it without thinking will usually knock you enemy back and give them a chance to escape. Either make sure you are behind them (which is easy with the slow from TO THE SKIES!), or to the side of them, preferably not the side of them that will knock them back towards river, as that is a good escape also.

THUNDERING BLOW is a great move for defending and peeling for your AD Carry, as it knocks the Assassin back away from your ADC, and back into any AOE damage in the center of the team fight.
This technique is also good for knocking the enemy AD Carry into the fight if you can get behind them, which I tend to do by waiting in brush, or AC GATE and TO THE SKIES!

I have found that most AD Carry's can still nuke Jayce in 3-4 hits when they are full damage items at endgame. But Jayce can also do the same to them, with AC GATE + SHOCK BLAST, followed by HYPER CHARGE. This works as the damage from SHOCK BLAST will usually do 1/4 of their health, and the increased damage and attack speed from HYPER CHARGE will out-damage them, and fire faster then they can.
Most ADC's won't expect this, and because Jayce's range with the MERCURY CANNON is less than most ADC's ranges', it's usually best to stand and fight rather than attempt to flee and get caught once you're in their range.
(This is obviously situational, and will only come predictable with experience in these situations)

When fleeing or stepping back a little from a team fight, use your ACCELERATION GATE in front of you and your team mates, then once you are past it and have the speed boost, fire a SHOCK BLAST behind you and through the AC GATE. Even if you cannot see the enemies because of the fog. As with Blue Buff and / or Manamune, mana should never be an issue.

Do not leave the Manamune Passive on all the time, especially early or mid game. There is no point using it against minions. I will only ever trigger it just before a team fight, unless I have Blue Buff, in which case, leave it on for the duration.

I have found that Jayce works best when roaming and ganking with Caitlyn, Diana, Darius... Pretty much any ranged champion with range equal to Jayce, and melee champions that have a grab or pull in ability, as if they cannot get in range, Jayce can chase them down, slow them and knock them back into range for an easy kill.