Choose a good quality exterior latex house paint for painting your doghouse. Be sure that you do not use a lead based paint which would be harmful to the dog if he chewed on it.
Paint the house black or a dark color if you live in a cold climate. Black and other dark colors will attract and absorb the heat from the sun to help keep the dog warm.
Use white or a light colored paint on your doghouse if you live in a warm climate. White and other light colors will reflect the sun and help to keep your dog cool.
Consider treating the wood with linseed oil and not painting it if you know that your dog is a chewer and will mostly likely chew on the doghouse. Linseed oil is a good protector for the wood and is not harmful for the dog if ingested.
Apply one coat of paint to all sides of the doghouse using a paint brush. Leave the doghouse in a clean dry area until the paint is fully dry. Paint the bottom of the house too as a layer of protection between the doghouse floor and the ground.
Brush on a second coat of paint if needed after the first coat is thoroughly dry.