How should I protect an extension cord across a driveway or sidewalk?

Use a rubber cord ramp (also called a cord cover or cable protector). It’s the only solution that won’t damage the cord, won’t create a tripping hazard, and can survive cars driving over it. Taping or burying the cord causes damage or electrical shorts. Get a hinged-lid ramp for frequent access, or a simple open-channel one for semi-permanent use.