Your dog should have his teeth cleaned a few times per week, so doing it at home is much more economical than taking him to a professional. Dog toothbrushes and toothpaste are available at most pet stores, so stock up on what you need and start young -- the earlier you get your dog used to brushing, the better.
Dogs don't always like it when people go in their mouths, so you may need to warm your dog up to the process over the course of a week. The ASPCA recommends dabbing a treat paste or even his toothpaste on your fingers, then gradually working your fingers into his mouth, massaging his teeth and gums with your fingers. This helps ease him into the brushing process. Once your dog is used to having your hands near his mouth, you can introduce the brush. Use only a toothbrush and toothpaste formulated for dogs, and brush his teeth for increasing periods of time over the course of a few weeks. For the first few days, he may only last a few seconds before giving up, but lavish him with praise. After a few weeks, he'll allow you to brush his whole mouth without much resistance, and you can more easily prevent the buildup of plaque.