Norway has a lot of camp-sites where you can stay in a tent, small cabin or mobile home. These can be found in almost all of Norway, even in very remote areas.
There are several websites that offer information about the camp-site prices, different accommodation options and locations.
If you are really serious about traveling to Norway on a budget, camping will help you save a lot of money. Bringing a tent or an RV means free (or close to free) accommodation, which is normally one of the biggest expenses.