Train from Nuremberg to Amsterdam

The Deutsche Bahn. You won't be able to buy tickets for next December yet (I think you must wait until June), but I found at least some trains listed for early June. Note that fares are likely to be much lower if you buy your tickets early. As time goes on and other passengers make their purchases, the least expensive tickets will sell out and only costlier ones will remain.

Renting a car in Germany and dropping it off in the Netherlands (if that's another option you're considering) will almost certainly involve a very expensive international drop charge.

www.bahn.com or www.ns.nl for buying a ticket or researching connections, and seat61.com for additional info on trains in Europe.
You cannot yet book tickets for December, though.

As above, the DB (German Railways https://www.bahn.com/en/view/index.shtml ) or NS (Netherlands Railways https://www.ns.nl/en ) sites. Takes 6½ to 7 hours with one change.
You can't buy tickets yet, but train times are already fixed up to the annual timetable changeover on 2nd weekend in December (Sat 12th).
Times after that will not be published until Oct/Nov, you can safely assume the trains will be similar if not the same.

For info about this route, see here: https://www.seat61.com/international-trains/trains-from-Amsterdam.htm#Amsterdam-Germany

Is there a reason you have to take the train? I'd fly. That's a fairly cheap ticket. The train takes 7 hours, the flight is just over an hour. That's basically a whole day you could use to look around.

I was indeed surprised to see that there are several direct flights a day between the two cities (I would have assumed one needed to go to Munich). So, unless you really like trains or are (rightfully) concerned by the environmental impact of flights, flying does look more time-efficient. And probably not more expensive.