At campsites, you can bring your own tent, caravan or motorhome, and there are also cabins for rent in several places.
Contact the site to find out about available places and prices.
You can find the campsites here:

Campsites in Kolding

Campsites in Billund

Camping passes are no longer a requirement in Denmark.
If you still want to buy a camping pass, you can buy this at the local campsites or on the FDM website if you are a member.

On the Naturstyrelsens website you can find rules and places for free camping in nature.