I am by no means an authority on this (or any) subject, but my mom and dad have found and returned a number of lost dogs, and here are a few things they have learned, which you may find helpful:
1. Try to secure the dog to keep it safe until you can find its mom and/or dad. Mom usually keeps a spare leash in her car; dad just takes off his belt and loops it through the dog's collar. Don't put the dog in a yard or pen unless it is SUPER secure. (Keep in mind that the dog may be an escape artist, which may be why he is out roaming around to begin with.) Mom once found a little beagle name Pal who managed to wiggle his way out of the back yard while his owner was on her way to pick him up. Luckily mom was later able to apprehend the little guy, after he roamed around the neighborhood for about a week, but she felt really bad for letting him get away in the first place. Don't just grab the dog. My dad learned this the hard way when a scared little min pin bit his finger badly enough to require a trip to Patient First. A lost dog is probably frightened and stressed and may be injured, so be very careful in approaching him or her. Try to get the dog to come to you with treats and soft coaxing. If you are unable to catch the dog, or if you think the dog poses any danger to you or anyone else, contact your local Animal Control department for assistance.
2. Check the collar for tags or identification embroidered on the collar. If the dog has an identification tag with the owner's name and phone number or address, that makes things very easy.
If there is only a rabies vaccination tag and/or dog license, you can often locate the owner by calling either the veterinarian who issued the rabies tag or the locality that issued the license. Usually records are kept with vaccination tag numbers and license tag numbers and the contact information of the dog's owner. Mom has found dog owners using both of these methods. Unfortunately most veterinarians and local government offices are only open during business hours. Also some may not want to give you the contact information of the owner directly, but they will take your information and contact the owner themselves.
3. If there is no identification on the collar or tags, take the dog to your nearest veterinarian (or emergency veterinary hospital, if after normal business hours) and ask them to check for a microchip. Most veterinarian offices are happy to do this. They may not want to give you the owner's contact information directly, but they will take your information and contact the owner themselves. Mom has found the owners of a couple of dogs this way. Many local Animal Control departments also have microchip scanners.
4. Contact your local Animal Control to report that you have found the dog. Even if you prefer to keep the dog yourself until you find the owner, you should contact your local Animal Control department to report that you have found a lost dog and provide a description of the dog and your contact information. Animal Control is often the first place people call when their dog is missing, and they usually keep records of reports of lost and found dogs. If you are unable to keep the dog, most local Animal Control facilities will keep it for a period of time until the owner is found. (The laws on this are probably different in every state regarding the amount of time Animal Control must hold a dog before trying to adopt it out.) Most local Animal Control departments will try their best to help reunite people with lost dogs -- this is much easier and less costly than boarding and finding new homes for them, or the alternative.
5. Take a photo of the dog and post it everywhere you can. Post it on Facebook and ask people to share. Make a flier and post the fliers around your neighborhood and at local veterinarian's offices and stores. Some newspapers even will provide free ads for lost dogs.
Mom and dad have found LOTS of lost dogs, and they have been able to locate the dog's owner every time, except for once. That one time involved a cute little male min pin that mom called Rudy after Rudy on Survivor (because he was a really tough little guy). (Yes, this was the same min pin who bit dad.) When mom and dad couldn't find the min pin's owner after several weeks of posting fliers and advertising in the newspaper, they contacted a min pin rescue group. The rescue group already had a list of homes they had approved who were looking for min pins, and Rudy was quickly placed into a forever home.
6. If you can't find the dog's owner, and you need to find a new home for him, you have several options. You can contact your local Animal Control department, your local SPCA, or other local rescue groups. If the dog is a particular breed, find out if you have a local breed-specific rescue group for that particular breed. Some rescue groups can arrange transport, so if you are unable to place the dog locally, you may want to do an internet search of rescue groups to include ones which aren't in your area.
We hope this is helpful!