Well, you found and chose an airline or two to fly you from Asia to Copenhagen among a few hundred airlines, you'll soon learn a handful of train operators out of Copenhagen.
But do study the cph public trannsport zone map with its 99 zones before buying your monthly fare, you may not need zone 4/airport for your daily transport.
For international the vast majority of schedules can be found at the german
www.bahn.de, or for good ideas check the_man_in_seat_61 og rome-to-rio. Please do not join the crowd that claims railway travel is terribly confusing.