You can purchase stencils and paint specifically used for painting on ceramic. It is easier to paint on ceremic mugs if the mug is laying on one side and you paint one side at a time, allowing drying time.
First remove any random items on the mug such as stickers or wire. Clean it with rubbing alcohol, lightly paint your design with acrylic paint and wait to dry.
I think there is a special paint to put on them. You will need to get a book on the subject, that might help you out. You can ask the people at the store which paint you can use.