I'm not sure of the definitive answer to your question about determining whether the land is private or not, and much of the Adirondacks are on private land. That that is public is often labeled as state land in some way. Many areas have wild camp sites that are actually designated.. These are usually along a dead end road, and have a pull out and a fire ring. I'd contact the ranger's office to find out where you can camp. I had a long talk with one when in the Adirondacks recently, and he was very friendly.