Yes, there is a stroke called the dog paddle, but it isn't necessarily instinctive for your dog. Like people, some dogs are good swimmers and some aren't. And dogs do drown. So if this is your dog's first time swimming, start slow and in shallow water. Don't push him to go deeper until he's figured out how to swim properly.
Swimming pools present another problem. Even dogs that are great swimmers often can't figure out how to get out of a pool. Before you let your dog jump in a pool to cool off, you have to teach him how to get out of the pool safely. This involves showing your dog where the shallow end and the steps are. It may take several times to teach him where he needs to go, but be patient--he'll get the hang of it. If the pool doesn't have a shallow end and steps, don't let your dog swim in it. In any case, keep your dog away from the pool when you can't watch him.
Swimming in rivers and in the ocean present problems such as strong currents and undertows. If you're doing any swimming with your dog, consider putting a life vest on him that is made especially for canines. And if you're planning a rafting or canoe trip, use a life vest because a strong current or rapids can pull a dog under very quickly. Your dog might also benefit from rubber dog boots (available through pet supply catalogues and on the Internet) if the river or lake bottom has sharp rocks.
When you and your pooch are done swimming, it's time to shower--that means your dog too. Chlorine or salt water salt can make his coat a mess, so be sure to rinse him off well and use shampoo and conditioner on his coat just as you would on your hair. Use a special pH-balanced shampoo and conditioner for dogs so that you don't dry his hair out. If it's warm, you can let him air dry, or use towels or a hair dryer made for dogs. (Don't use human hair dryers--they can burn a dog's sensitive skin!)