When I bought this Passat, the seller wanted to keep her license plates. They were vanity plates, with her initials.
So she unscrewed them from the car and kept them. She very kindly gave me the screws too.
So I drove the car home with no plates. It's not such a big deal: maybe 1% of cars on the road at any given time have no plates. But they usually have an ad for a dealer there, and a piece of paper in the windscreen saying that they have actually recently bought the car, and the plates have been applied for.
But I didn't have that - this was a private sale. But I drove it anyway. It's very law-abiding here, but also pretty forgiving. (For example, illegal^Wundocumented immigrants can't get driving licences, so it's illegal for folks in that category to drive ... but in practice, you have to drive, so it's not the big deal it would be in the UK. More on this later.)
Anyway, the seller has to fill in a form if she wants to actually keep ownership of the registration number. (But that's not my problem.)
I went to the DMV. In Los Gatos, since you ask. Queued up for a bit. Probably should have made an appointment - might have saved half an hour.
Anyway, I filled in a form, wrote them a check (sic) for four hundred and something dollars (tax gets paid pretty much whenever a car changes hands, based on the sale price...), and went to another window, where they gave me plates and stickers ("tags"). I had a screwdriver in the car, so I screwed them on and stuck on the stickers when I went outside.