There's more than one cruise terminal in Copenhagen - Ocean Quay is the newest one, and is north-east of the city centre.
From Copenhagen Central Station you can take a surface train to Norreport station, then a short taxi ride to Ocean Quay.
But my niece and I chose a more scenic route. We joined the red Hop on Hop off bus in the city centre and took it all the way out to Ocean Quay. The bus staff are used to passengers coming on board complete with cruise luggage! After a lovely tour of the city, the bus stops right at the Princess Cruise terminal.