When the revs are matched the gears will connect nicely with or without synchromesh. Synchro allows lazy drivers to get away with all sorts of abuse. Or rather, what would be abuse with a crash box is now ok.
It's not about slamming the gears in or dropping the clutch. When you throttle off to shift up, the revs drop naturally. So shift quickly to match the revs. Shift slowly and the revs will have dropped.
Going down a gear, mismatch the clutch and throttle so the revs blip and shift a fraction after while the revs are up. Most people shift down slowly. Sometimes, you'll see the car lurch especially on hills as the forward momentum pulls the engine revs up to speed.