A NemKonto account is any preexisting bank account you choose to register. It is an account that Danish authorities and private companies can pay money owed to you into. No money can be taken out of your NemKonto without your consent, but money can be payed into it automatically.
You can choose to register a Danish account or a non-Danish account as your NemKonto. Registering a NemKonto account is free.
Registering a Danish account is easy. You simply contact your Danish bank and ask for your Danish account to be registered as NemKonto.
Registering a non-Danish account is a bit more complicated. You need to fill out a form from NemKonto which you can download here. Upon filling out the form you send it via regular post to NemKonto. Be sure that the name that you put on the application is the EXACT same name that is on the account you wish to register. If the account is a shared account (eg. with your spouse), it is important that your name is registered on the account alongside with your spouse. Once registered with NemKonto, you will receive a letter with a confirmation code that you should use to activate your NemKonto.
NOTE: Make sure that the last municipality (kommune) in Denmark you lived in has your new address. Otherwise the letter with your confirmation code will be sent to your last known address in Denmark.