Generally speaking, you stay in ranged the majority of the time. His Hammer form is primarily there as an added form of burst damage (R into Hammer -> Q -> AA -> E -> disengage). Jayce is awkward in lane since his QE leveling pattern (that is, skip points in your ult and W) gives him weird spikes in power until Level 11. Likewise, he won't really 100-0 straight up but he can Cannon QE combo over and over while staying safe so he has high kill potential in lane ... eventually.
Item wise, I wouldn't suggest finishing Manamune early on him. Tear -> Damage item (Brutalizer, typically) and then Manamune-> Last Whisper is usually how he goes. Manamune works if you plan to focus more on landing QEs repeatedly but, honestly, you can do that with just the Tear anyway. And I would't bother with the super late game TF.
As for late game, you basically just Cannon QE over and over and then Cannon W with Muramana going when you shoot the squishy for maximum damage. Use the Hammer QE only if it'll guarantee a kill or if you need the knockback for peel. Don't try wading into fights like he's a bruiser since, yeah, you just build him raw AD glass cannon.