Bus 5A will take you directly to Copenhagen Central Station, City Hall Square, Nørreport and other stations. It takes about 30-35 minutes from the airport to the Central Station.
The bus runs every 10 minutes at day. The bus runs all night as well, but not as often.
Tickets can be bought at the ticket machines in terminal 3, or you can buy a ticket on the bus. Please note that the bus drivers only accept coins.