You can buy tickets in the ticket machine uding credit card or cash (dkk). From and to the airport the train is easiest to Ørestad. The train departs from the airport downstairs. You can not buy a return ticket - but just but it in the machine before departure. It should be 24 dkk for the ride from airport to Ørestad.
The trains depart every 10. minute - 20. off peak and maybe less frequent in the night. Check journeyplanner.dk or use google maps.
thanks for your reply your link to the transport system is very helpful.
thanks for your reply the information you gave is very helpful.