The Copenhagen card is available at the train ticket counters at the aiport.  It can be purchased in 24 hour denominations and the person selling it will ask when you want that time to begin and mark the card, accordingly.  The best thing about it is that it makes all manner of public transportation (metro, train and bus) completely paid for within that period you purchased, it also grants free access to many tourist locations. So, it gets you there and in the door.  For a complete list of free admissions,

 http://www.copenhagencard.com/free-at...

 

You just show your copenhagen card when asked on public transport or at the door of these places.  Easy