To get a campsite, make sure to purchase a Camping Card Scandinavia (valid in Denmark, Sweden, Norway and Finland) before you go camping, or at the first campsite you visit. It's reasonably priced and is valid for the whole year. There are discounts for single overnight stays, and groups of 5+ campers.
Camping in Sweden
The Camping Card Scandinavia (SEK 125) lets you camp in Sweden easily. The "Camping Card International" is also accepted at many campgrounds in Sweden. In Sweden, it is permitted to camp in free nature (camping on private property and having camp fires is restricted.)
Camping in Denmark
A Camping Card Scandinavia is needed to get a campsite. Camping in Denmark generally costs DKK 45-65 per night during the high season and is cheaper in spring and autumn, naturally. Pets are allowed at most Danish campsites but may cost extra at campgrounds in Denmark.
Denmark also has nudist camping, visit the Danish Naturist Union for more information.
Camping in Norway
In Norway, you can camp anywhere outside of towns (except on farmland) for 48 hours max, without open fires in summer. If you're heading for one of the campgrounds in Norway, get the Camping Card Scandinavia mentioned above. Pet-owning campers note: Because of rabies, it's not allowed to bring animals into Norway.
There are three nudist locations in Norway - contact the Norwegian Naturist Federation (NNF) at +47 959 64 689.