The treatments I have outlined below are for first-degree burns. Dogs with second and third-degree burns should always go to the vet. Infection can sneak up quickly and proper treatment should be administered right away. With all types of burns, you should always monitor your companion making sure he/she has not gone into shock.
If your canine has a second or third-degree burn, gently wrap the area with a bandage. Do not use a bandage with loose fibers! These fibers could imbed into the burn and cause more problems. After the burn has been wrapped, seek medical attention. Ointments and creams should not be used on any type of burn (Especially, second or third) unless directed by a veterinarian. It doesn't really help the healing process and could cause more problems than worth.