All the good Jayce's I see start combat in ranged mode to get of his e-q combo. Once and only if that lands, you follow up with w-r-w-q, saving E for if you need an escape or to zone.
Essentially that combo breaks down like this, you lay your gate and shoot a charge through it to get the first burst, then you activate his steroid, and then switch to melee to activate his aoe. You do this while running through the gate and suddenly you have crazy gap closing and dps potential due to his passive and r passive (which deals bonus magic damage for the first hit). You then use your q to continue your gap closing and lay a CC and to follow up the second part of your burst with three quick melee attacks, while the aoe rounds off the damage. At that point, they should be low enough that you can finish them off, force a retreat or then you use E to force a disengage to set up for a second volly. You can also pursue them in ranged mode to get an extra aa or two if they retreat. This is an ideal scenario though, but that's the jist of how his combo works.