If you are being poked under your tower, quickly casting To the Skies!To the Skies! on a group of minions will clear them and damage your opponent. While they are slowed, you can use Thundering BlowThundering 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.
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 inadvertedly 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 a 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.
Although his poke in the form of Shock BlastShock Blast is highly damaging, the projectile from this ability is slow and relatively easy to dodge. He can enhance the attack using his Acceleration GateAcceleration 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 BlastShock Blast has an AoE effect that can damage you through a line of minions.
To the Skies!To the Skies!, even though it is a targetted 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.
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 布里茨的Rocket GrabRocket Grab and 诺提勒斯的Dredge Line 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 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.