The easiest way is to take either the metro or the train. Both can be taken at the airport, alternatively you can also take bus 5C. The metro serves more areas of the city, whereas the train takes you to the Main Central Trainstation (Danish: Hovedbanegården).
Therefore it really depends which area of the city you will be residing in. We recommend you check either Google Maps or the Rejseplanen app.
The station at the airport is “Kobenhavn Lufthavn”.