Keeping a dog in good health is not difficult. It is important that you feed them a well balanced diet, good quality food, a variety of dry and wet foods as well as a hard bone to keep their teeth strong.

[edit] Steps

Feed your dog high-quality, well-balanced dog food and treats. This is your pet's main source of nutrition. A vet may tell you "If you can buy the dog food somewhere other than a pet store or vet's office, then it is probably not the best meal for your pet!" However, keep in mind that few veterinarians have received more than a minimal amount of training in nutrition as part of their veterinary degree. Today, there are numerous high quality pet foods being sold online directly to the consumer, bypassing the vet's office.
Examine the first 5 ingredients listed on the pet food label. These ingredients generally make up the majority of the food. Look for meat and vegetables, rather than meat by-products and grain fillers. Corn, rice, whole wheat, barley, soy and other grains are cheap sources of protein used by many commercial pet food producers as a clever marketing ploy to increase the percentage of protein in their feed. However, these are often difficult for your dog to digest and do not promote optimal health.
Be aware that, in the U.S., current pet food regulations allow pet food manufacturers to include materials from dead, dying and diseased animals in their food. Roadkill, diseased animals as well as animals which have been euthanized are legally used pet food manufacturers. "By-products" can include chicken and duck beaks, feet, bones and intestines. To learn more about what your dog food is really made of, you can watch an informative video offered online by holistic pet food manufacturer HealthyPetNet.
Avoid pet foods that contain chemicals, preservatives (BHA and BHT, artificial colors and flavors. The healthiest food for your pet is made from a proper balance of "human grade" materials.
Give your pet "human grade" food. But that doesn't mean you should give your pet every food you would eat. Some food that is good for you may be toxic to your dog (including onions, chocolate, grapes, raisins, and more).
Maintain your dog's weight at a healthy level. Obesity in pets is every bit the epidemic that it is in humans today. But the added stress of being overweight will shorten your pet's life.
Provide your dog with a constant supply of fresh water.
Groom your dog regularly. Brushing your dog's coat encourages good circulation and will help keep your pet's coat shiny and healthy.
Clip your dog's nails regularly. Once accustomed to the procedure, most dogs will allow their owners to clip their nails at home with inexpensive clippers available at most pet stores. However, if your dog resists, you may find it better to allow one of the technicians at your Vet's office clip their nails. It is important to clip only the white part, to avoid hitting the "quick" which will result in bleeding.
Check and clean your dog's ears on a regular basis. Again, this is easily done at home. There are a number of products readily available to help wash diret and debris out your pet's ears gently, but avoid any products containing alcohol (too drying).
Monitor your dog's dental health and provide appropriate dental care. Give your dog healthy "bones" and chews that will promote healthy teeth and gums. However, make sure to give him a safe, fully digestible product (such as porkhide bones, rather than traditional rawhide) and never give your dog cooked bones of any kind. Your Vet can provide you with instruction on how to brush your dog's teeth if your pet experiences tartar build up.
See a reputable Veterinarian regularly and keep your dog's vaccinations up-to-date.
Make sure your dog receives adequate exercise. Depending on the breed, this could be anything from 10-15 minutes per day to a good hour romp in the park. This will cut back on bad behavior, such as tearing things up around the house, and aggression.
Socialize your puppy once he has had all his important first vaccinations. Take your puppy to your local library on a Saturday morning, sit on the steps, and let every person who shows interest pet, hold and fuss over your dog. Let your puppy socialize with other (non-aggressive!) dogs. A puppy kindergarten / doggie daycare program is ideal for this. The more unique social situations you expose your pup too when they're young the better.

[edit] Tips

Maintain a record of your pet's key information (name, age, breed, description, licence number, vaccinations, etc.) as well as a photo of your dog. Not only is this information helpful to your pet sitter, etc., but it will be vital should your pet ever become lost. You can download an example of a Pet Record here.
Consider having your Vet implant a microchip for identification as well.

[edit] Warnings

No matter how right and natural it seems at first, never feed a German Shepherd pork and saurkraut.
Do not give your pet cooked bones! They are hazardous and can give splinters in their throats!