A wasp sting can be very painful but unlikely to cause an allergic reaction. Treat the affected area with ice cubes held to the skin and watch for the redness to go away. Benadryl is normally not recommended for dogs but you can consult a veterinarian to see if it would help.
A wasp sting affects a dog similar to how it affects humans. If there is a stinger, pull it out. Clean the wound. Some dogs may be allergic and may need treatment. I suggest some pain medication and benadryl.
As with humans, wasp bites can be dangerous for dogs allergic to a wasp sting. In most cases you should immediately seek the assistance of a licensed veterinarian.