Copenhagen is the capital of Denmark. The airport ( http://www.cph.dk ) is situated 10 Km. from the centre of Copenhagen. There is a train connection from the air port  to the central station.  The entrance to the train station is from Terminal No. 3. Buy your ticket on the ground floor ticket office.

From the central  station ( http://www.dsb.dk also English version) there is train connection to the rest of Denmark. You can also get on the subway train covering the greater Copenhagen. Busses are used for local transport. Long haul bus routes are almost non existing. Use the route planner ( http://www.rejseplanen.dk ) to get you onwards.

The majority of tourist  therefore drive to Denmark bringing their own car. From the south you can drive up through Jutland, and use the bridges. Keep in mind the Great Belt bridge has a toll of Euro 30.  Or use the Roedby / Putgarden ferry from Northern Germany.