While picking out a puppy is very much a matter of the heart, there are a few things to keep in mind while looking for a four legged friend to add your family.
The optimal age for getting a puppy is when it's between 8 to 12 weeks old. By that time the pup should have had its first series of shots, be socialized, and weaned. If a puppy is lethargic and too skinny, it's obvious there is a problem. However even puppies that look hale and hardy may have some condition so give them a general inspection.
Their eyes should be clear, with solid irises. White spots or visible lines could indicate genetic eye conditions. The nose should be cool. If the puppy is sneezing or has runny eyes or nose that could be a sign of a problem. Check the teeth. Even with just their baby teeth, you can get an idea if their bite looks right. The dog's upper incisors should slightly overlap the lower ones. Gums should be a healthy pink color. Pale gums are a danger sign for anything from anemia to parasites. The top of the skull should not have any soft spots.
The fur should be soft and the skin underneath smooth. The ears be clean and smell clean. If you see wax and notice an odor, it could indicate ear mites. Similarly, if the puppy indicates discomfort when you touch its ears or shakes its head repeatedly, that could also be a sign of an ear infection. The puppy's breathing should be even and easy without any sounds of congestion or wheezing.
People looking for a show dog may want to discuss breed standards with the breeder but for those simply looking for a pet, making sure it's healthy will be the top priority. If possible make your purchase price conditional on the puppy being in good health and not suffering from giardia or other issues that may require treatment.