To clarify things:

For AppleCare: I believe you have to notify Apple in writing. If you call the AppleCare support number they will give you the details.

For the standard 1-year warranty: No action is necessary. I called and confirmed this myself when I got my iBook G4--I had already used up my 1 educational purchase for the year but I needed another computer. So I had my girlfriend purchase it with her educational discount and then give it to me. The Apple person I talked to said no problem, there's no action required.