A new driveway needs very little maintenance, but the first few weeks are worth a bit of care.
Tarmac
Keep vehicles off for around 48 hours. For the first few weeks avoid turning the steering wheel while stationary, since that scuffs a fresh surface, and try to keep motorbike stands and caravan legs off it or use a spreader plate. In hot weather a new surface softens slightly, which is normal.
Block paving
Expect to top up the kiln dried jointing sand once or twice in the first year as it settles. Sweep rather than jet wash the joints, since a pressure washer held close will blast the sand straight out.
Resin bound
Sweep it occasionally and wash it down now and then. Avoid dragging metal edges across it, and use a plastic shovel rather than a metal one if you clear snow.
All surfaces
Deal with oil and fuel spills quickly, keep drainage channels and gullies clear of leaves, and cut back anything that overhangs and keeps the surface permanently damp.
If something does not look right, tell us early. A small issue caught in the first year is nearly always simple to put right.