There are a lot of issues that you'll have to worry about when you're picking up a stray dog, but if you have called the local animal control and no one has claimed the animal, you can keep it to be a pet as long as you get it the necessary care. There are different things that you'll want to have done, and you'll want to go to the veterinarian's office so the dog can be looked at. Consider the following options.
One of the first things you want to do is have the dog dipped for fleas and tics. This is a special bath where they are treated for any live adults or eggs that are currently living on the dogs body. This is important if you worry about the dog bringing fleas around your cat or other dogs or into your home.
Vaccinations and Heartworm Pills
Since you don't know if the dog has even been vaccinated you want it to have all of the necessary vaccinations. You'll also need it to get a rabies shot in order to get the dog registered with your local animal control or city authorities. The heartworm pills are also an easy way to get your dog the heartworm protection it needs.
Stool and Blood Testing
Testing the stool will help determine if the dog has parvovirus or worms. Getting the blood work completed will detect other types of illnesses and health issues. You will want to get a fresh stool to take with you when you go to the appointment.
If the dog doesn't look like it has been groomed or the hair and nails are long, schedule a grooming session to have the haircut. You may also want to get a teeth cleaning for the pet and a dental inspection to see if there are any dental problems to worry about.
These are just some of the services that you can have completed at the vet's office. If you worry that the dog isn't behaved, or that it may have some aggression problems, you'll want to sign up for classes and have the animal assessed by a dog trainer. The dog trainer can do a temperament test and see how the animal acts around other dogs and people and see what classes are needed. Make sure the stray isn't a health risk in your home by taking it to a veterinary clinic like Apple Valley Animal Hospital.