Hello! I'm PodzyCA and this is my guide to playing Jayce. Jayce is a versatile champion with a wide array of abilities, but this is how to play him as a solotop. This guide is mainly meant as a generic item path to show players how to build Jayce for success in the top lane.
Jayce is, in my opinion, best to be classified under the archetype of offtank, since he can soak up damage and also dish it out. Jayce's abilities, such as his Thundering Blow (E hammer form), allow him to deal damage without needing to build damage items. Other abilities, such as his Acceleration Gate (E Cannon form) and To the Skies (Q hammer form), allow him to put his allies in better position and quickly close gaps with the enemy.

When playing Jayce in lane, your main goal, like any other top champion, is to farm and keep the opponent from farming. The cool thing about Jayce many of his abilities have synergy with eachother.

Now to go over his abilities and what he can do.

When switching between mercury hammer and cannon, Jayce gains a bonus ability on his first basic attack and increased move speed for 1.25 after switching.

Mercury Cannon:
When switching into Mercury Cannon, your first basic attack will lower the targets magic res and armor by for 5 seconds.

Shock Blast:
Shock Blast deals damage in a small radius around its collision point or at the end of its range. It can collide with any unit, and not with terrain. it also reveals the area it effects. It can work in synergy with Acceleration Gate and To the Skies. Acceleration Gate boosts the missile speed, damage, and AoE of Shock Blast. It can give vision of targets over walls, allowing you to jump to them with To the Skies. This should be the first ability to max, as it can one hit caster minions at level 4 (champion level 7) through Acceleration Gate, allowing you to farm well from a distance.

Hyper Charge:
Boosts your attack speed to maximum for 3 basic attacks, while reducing the damage at lower levels and boosting it at higher. This also means that it can reduce or boost the damage from Mercury Hammer swap in damage. This should be maxed second, as it allows you to push turrets more quickly and deal damage more quickly.

Acceleration Gate:
Boosts movement speed of all champions who pass through it. It can work in synergy with weapon swap, as acceleration gate boosts speed by a percentage, including the gain from weapon swap. It can be used to chase and get back to lane more quickly, and, of course, with Shock Blast. It can also be used to gain assists and help allies chase, as boosting the speeds of allies who attack or kill enemy champions will also give you an assist.

Mercury Hammer:
Increases damage on the first basic attack, working in synergy with Hyper Charge. Also, while in hammer form Jayce has increased defense and MR

To the Skies:
Slam Dunks the target with your hammer, slowing their movement speed and closing the gap. This can be used with Thundering Blow, as you can hop to or behind an enemy and knock them wherever you want them to go with Thundering Blow's knockback.

Lightning Field:
Damages enemies around you, and gives you mana on basic attacks with Mercury Hammer. The mana gain works with any basic attacks, against structures or units.

Thundering Blow:
Smacks an enemy for a percentage of their health as magic damage and knocks them away.

Jayce can burst pretty hard with all of his abilities, and still deal damage afterwards. With so many abilities, the order can get a bit difficult but it's fairly simple once you try it a few times.
Playing Jayce as an offtank means that you are both dangerous and deal damage, but also that you need to protect your squishy allies (I refrain from saying carries as Jayce can also be seen as a Carry even as an offtank). Since Hammer mode gives you additional resistances and Cannon mode lets you engage from a distance and allow your allies to move faster, you should enter teamfights and lane mostly with Cannon mode. Once you've done your initial burst of Acceleration Gate->Shock Blast, Hyper Charge before switching to Hammer Mode and engage with To the Skies and Lightning Field, and aim to either kill or re-position an enemy with Thundering Blow. Thundering Blow should be used early or late in a team fight, as it adds a great deal of mixed damage to your burst, but it also knocks enemies away, which might accidentally save them in a chase (although it's not too difficult to last hit an enemy with the E->Q combo).
When poking or ganking with Jayce, it's essentially the same as team fighting. You come in with Cannon mode and lay down Acceleration Gate to boost your Shock Blast and yourself and W before switching to hammer, come in with To the Skies and Lightning Field, and knock the enemy away from you before he can damage you or away from help/turret side if you're going to kill.

I call these build directions as these builds should not (though can) be followed exactly, nor should they be followed exactly in this order. The purpose of this guide is to give an outline of what offtank Jayce should look like and how to play him. Certain items like Triforce build really well on Jayce and for that reason are essential on both guides, while items like Atma's or Frozen Mallet can be substituted for other items depending on the enemy team or the situation you're in. The first build is meant to deal more damage but is not tanky as the latter build. Whichever direction your team requires you to go in is which kind of offtank you should fill.

That's basically it. Have fun with Jayce, he's incredibly cool and incredibly fun and versatile and many other awesome things.

:D