There is no permit needed to purchase a gun in Wisconsin. There is a 48 hour waiting period for a firearm. Firearms dealers must have detailed information on the person purchasing the gun. "The people have the right to keep and bear arms for security, defense, hunting, recreation or any other lawful purpose."
Some states require that a citizen acquires a permit, before they purchase a gun. If it is required, there will be a fee that varies from state to state. Some states also require finger printing, and background checks before issuing the permit.