Run tele and flash and start longsword 2red 1blue pot. Play passive in lane and use q to farm if getting pressured until 700-900 gold. Within that gold window, reset the lane and then b, buy tear, and start running back while transforming and using w in each form. If necessary, tele back in.
Standard harass shouldn't start unless you're certain you can manage mana issues (basically when you get tear) or if you're sure to not be ganked, because jayce poke pushes the lane. E>q is standard in cannon form, aa>w isn't worth it half the time, just q is still powerful. Hammer fom is riskier, but standard combo is, for harass, starting hammer, q, aa, e, transform, e, q through e. Near impossible to retaliate without cc. Standard all-in is, starting cannon, e, q, transform, q, aa, e. Jayce isn't great in extended skirmishes until muramana is finished, so he mainly just pokes or does an all-in burst with e to disengage.
I find he's better playing passive until midgame or grouping, because his siege potential is godtier and his power spike occurs around level 9.