Yes, your dog can get sunburned and, just like with human sunburn, your dog can get skin cancer from too much sun exposure. So as much as your dog loves to sit around and play outside, you do want to protect your dog when he is under the sun.
The first option is to limit the amount of time your dog is outside; however, this may not be practical or even desirable for the quality of your dog's life. So a second option is doggy sunscreen where he needs it most. Dogs are most vulnerable to sunburn wherever their fur is lightest, such as on the nose and tips of their ears. Also, dogs with white or light-colored fur, just like fair-skinned humans, are generally more susceptible to sunburn, as well. You can use zinc oxide on these vulnerable areas, or even buy doggy-specific sunscreen at your local pet goods store. Be careful when you apply the sunscreen on your dog, and don't let him lick it off.
You'll know if your dog does have sunburn because it looks pretty much the same as sunburn on a human. Your dog will have reddened skin that may also be peeling. He might even have some blisters. If your dog does have sunburn, it will heal itself but you'll want to help lessen the sensitivity and rawness of the area. The first thing you can do is to lightly mist the area with cool water. Lightly placing a cool compress on the area can also help relieve the discomfort. As the compress warms up, simply refresh it with cool water. If your dog's sunburn has broken skin or if your dog is visibly in pain, you might want to take him to the vet.