Stray animals seem to abound in our society. Determining whether an animal is lost or simply wandering can be a major test of your discretion. Too many times I have seen kind hearted good-doers create havoc by picking up a dog as lost when it wasn't. Try to make sure an animal is truly lost before you take action. When an animal is in danger then act. Get a dog out of traffic or away from danger, but don't be so certain that he or she is lost. If the animal has tags with a phone number, call the owner. When you live several miles from where you have found a dog, you may simply want to tie it up in a visible place and give it water. At grocery stores, many dogs will jump out of a car window while the owner is shopping. To haul this dog 15 miles away to your house is creating far more problem than it is solving, tie it up near the door. If you can check back in an hour or two do so, if not, you have still done the dog more good than arbitrarily hauling it off.

When a dog or cat is found and it is quite obvious that this pet is lost, try to get it in your car or if you are walking put a leash of some sort on it.
Obviously when an animal has tags you will call the number on them. A license or vaccination tag will lead you to the owner through the veterinary clinic, county or city that issued them. The most considerate thing you can do at this point is put a sign where you found the pet. If it appears to be a valuable animal, simply state "FOUND black and white dog" call to identify. Don't let a dog napper know you have found a purebred female afghan hound.
You may want to drive around and look for lost pet signs, as you are the one person that the signs were made for.
When a pet has no tags you may want to call animal control to pick the pet. If they are closed you may be able to drop it off or else try to make it comfortable at your home. I suggest your garage, as you have no idea how well trained he or she may be. Give it food and water and something to sleep on. Use a leash for relief walks unless you have a well fenced area for that purpose. Most pounds will only keep a dog or cat 3 days before euthanizing them. You may consider keeping the pet with you as he or she is probably more comfortable at your home than a pound. This is entirely up to you.
Call animal control. Most newspapers have a free "found pets" section so call them. Radio stations and some TV stations take lost pet messages. Hopefully the owner will contact you soon. Make any caller identify the pet and meet them at a police station or attended firestation. Be careful about letting a stranger come to your home.
If no one claims the animal and you don't decide to keep it yourself, contact you local humane society for options.

One very important note, on the chance that you find a pet that has been killed, don't hide it. If it has a collar with a number, try to contact the owner as they would appreciate knowing what happened to their friend, even when it is bad.