Jayce has a great variety of abilities at his disposal. Judicious use of different combinations grants him excellent flexibility, able to adjust for most situations.
It is best to start pushing a lane in cannon form first, using acceleration gate to create a more powerful Shock Blast, And when in close range switch to Mercury hammer and use To the Skies for an effective combo.
Placing Jayce within the Acceleration Gate and casting Shock Blast won't tip off the enemy of the exact line you'll be firing on as much since the projectile of Shock Blast will be instantly speed up, giving them less time to better react. As well, casting Shock Blast and then placing Acceleration Gate in its path can allow it to hit an enemy that wrongly assumes they can out-run the ability.
If you are being poked under your tower, quickly casting To the Skies! on a group of minions will clear them and damage your opponent. While they are slowed, you can use Thundering Blow to knock them back into tower range for a potential surprise kill.
Changing forms introduces an entirely new set of abilities that do not share the same cooldown timer with the other set of abilities. Changing forms twice will not cause an ability to go off cooldown any sooner.
As Acceleration Gate will also speed up allies in addition to yourself, casting it immediately in your team's path can help greatly when making a unified retreat or chase attempt.
Even though Thundering Blow does not scale off a target's missing health, it can be used as an execute-style ability. Keep your eye on the opponent's health and cast Thundering Blow when they have reached the same % of their health as it will deal for a safe kill.
Acceleration Gate reveals fog of war at either end of the gate, use this to help set up jumps on minion camps in the jungle.
While in lane if against a melee champion, be sure to continually harass them while in your Mercury CannonMercury Cannon form, this will deny their minion kills and help give you more lane control. Doing this will inadvertently push up your lane so stay at a distance once you've pushed up to a tower in order to allow for an easy escape from a gank.
Playing and building around Mercury HammerMercury Hammer is generally easier of the two as the transition from ranged to melee is an easier and less-risky one for a champion that has built significant durability items, while a transition from melee to ranged is obviously beneficial for chasing down targets or kiting enemies - and without durability items, one is unlikely to live long enough to allow a good transition from melee to ranged.
Trinity Force is an extremely useful item for Jayce regardless of his build, as he benefits at least moderately from all the stats it provides. He can proc its passive effects regularly as he will be making repeated use of his spells and autoattacks in combat.
Frozen Mallet combines well with Jayce's exceptional chasing abilities by slowing the opponent and making it extremely difficult to escape from him. It also grants a large amount of health, letting him stay in a fight for much longer.
Cooldown reduction can be a useful stat to itemize for on Jayce because of the utility and damage his spells afford him.
Jayce is highly vulnerable to ranged harass in lane due to his short autoattack range of 500 in cannon formcannon form, and most ranged attackers can reliably hit him without fear of return fire, as Jayce cannot benefit from the mana-gain-per-hit passive of Lightning Field without taking ranged harass should he run out of mana while in cannon formcannon form. Consider good poking top laners such as Kayle or Kennen to take advantage of this.
Although his poke in the form of Shock Blast is highly damaging, the projectile from this ability is slow and relatively easy to dodge. He can enhance the attack using his Acceleration Gate, but this makes his attack telegraphed, and lets you possibly enact countermeasures to it. You can also simply remain behind minions to block the shots. However, an accelerated Shock Blast has an AoE effect that can damage you through a line of minions.
Despite his good mobility, Jayce only has one hard gap closer in the form of To the Skies!. Strong slows like WitherNasus can enormously reduce his effectiveness in combat.
To the Skies!, even though it is a targeted ability, does not actually track enemies who are moving. A blink or dash ability used while he is in flight can dodge his attack and avoid his slow. You should try to save these escapes for when he is about to use it.
Most of Jayce's damage is physical. Buying early armor can help in mitigating his damage.
Stacking health against Jayce is less effective as his Thundering Blow deals a large amount of magic damage based on your maximum health.
When on the run from Jayce and his team, you can attempt unusual juking maneuvers in order to mess up his attempts to use Thundering Blow to knock you back towards his team.
You may need different strategies to deal with Jayce depending on how he is playing.
Carry Jayce can put out considerable damage with his abilities in Transform: Mercury CannonTransform: Mercury Cannon form, but the short range on his autoattacks means he must remain close to the front of a battle to make the most of his kit. This means he is highly vulnerable to attack from tanky champions such as Irelia or assassins like Akali. Even better, pulls such as Rocket GrabBlitzcrank and Dredge LineNautilus when pulled off can yank him into range of your entire team and quickly burst him down before he can dish out significant damage.
Jayce can use To the Skies! to cross walls and provide a surprise attack. Both denying him vision of key bushes by destroying any wards placed there and warding yourself to keep track of his movements will prevent him from abusing this.