Adopting from a shelter can be very rewarding for both dog and owner. Shelters have puppies as well as adult dogs, and there are a few things to consider.
Puppies are kind of blank slates, and you can kind of groom them, and train them to fit your lifestyle a little bit more.
Some adult dogs will come with some experience under their belt. The nice part about that, is that adult dogs will kind of already be set in their ways, maybe have some training already under their belts. The bad part of it is sometimes they'll come with a little baggage that need a little bit of work, need a little bit of training. You should know your experience level. Talk to the shelter staff. A lot of the staff is very knowledgeable, and can be very helpful in choosing the right dog for you.
Again, this comes down to size, shape, temperament. What are you looking for in your household? You can also find rescue groups that are breed specific. So, you can find Lab rescues, you can find Golden Retriever rescues, but for the most part shelters have a great variety.
You have to decide whether you want a pure-bred or if you want a mixed breed. Mixed breeds are kind of one of a kind, and their always fun, but you're not 100% sure what you're going to get temperament wise, or looks wise as opposed to finding a pure-bred dog, but shelters are a great place to find these dogs.
The staff at a shelter are very knowledgeable, and you should utilize those things to your best interest, and that's the way you would do it.