If I drive a car and ride a motorcycle, what do I do with a boat?

Once we have specific verbs to refer to the action of operating a vehicle, my question is:

What verb should I use to "drive" a boat/ship?

You pilot it. And on larger watercraft having an enclosed room containing the pilot’s wheel, that room is called the pilot house.

The verb was either borrowed from pilot (n.) or from the French piloter, according to Online Etymology Dictionary:

pilot (v.) 1640s, “to guide, lead”; 1690s, “to conduct as a pilot”, from pilot (n.) or from French piloter.

pilot (n.) 1510s, “one who steers a ship”, from Middle French pillote (16c.), from Italian piloto, supposed to be an alteration of Old Italian pedoto, which usually is said to be from Medieval Greek pedotes “rudder, helmsman”, from Greek pedon “steering oar”, related to pous (genitive podos) “foot”.

As others have pointed out, pilot (v.) has also acquired a specialized modern sense (“to lead a ship through a difficult or dangerous area of water”, Macmillan Dictionary) and pilot (n.) now generally means such a specialist. But the general sense of steering a ship is still in use today, just as it was in the 19c and 20c. This explains how the terms were borrowed by balloonists and airmen when those technologies came on the scene.

If it’s a sailing boat, you sail it. If you’re the captain of a ship, you skipper it, and if you’re the helmsman, you steer or helm it, but otherwise, there’s no general term. I did once hear a former captain of the Royal Navy aircraft carrier ‘Ark Royal’ say that he drove it, but that was in jest.