You may find it helpful to review this website which discusses lost pet behavior:
Leave food and water out in the same exact place at the same exact time every day.
When leaving the food and water, call the dog's name (if known) several times and follow it constantly with: "Good Dog!" in a very happy tone. If you don’t know the dog’s name, call it something else (puppy, doggie, baby) and be consistent with what you call it every day. Whether you see him around or not he may be watching and would hear you even if he doesn't come out just yet.
If you can determine the owners, obtain an object with their scent on it. Good examples are
an old t-shirt, glove, sock or shoe they have worn which smell like them. Leave the scented object next to the food.
When you see the dog, you will want to appear non-threatening while talking to it in a soft, calm voice. Get into a submissive position. Get on your knees or sit down. Keep your eyes cast down and smile while turning your head away at a 45 degree angle so the dog will only see one side of your face. This will make you seem less threatening to the dog.
When the dog approaches, turn your body slightly away from him even more - almost as if you are playing slightly hard to get. Make your movements slow and subtle and continue to talk to him in a low soft voice, saying 'good dog!'
Keep your hands in your lap with palms up and if you have a treat, hold it there for the dog. Do not grab at him. Let him come to you. This may take a while, possibly multiple tries over a few days. Remember, this dog may have been on its own a while so may not trust strangers.
If he seems responsive to a command, tell him: "Sit." If you can get him to obey a command, like sit, then tell him "good dog!" and then tell him "Come."
Remember to consistently provide verbal praise, make no fast moves, keep your body and eyes submissive, and use a low voice, soft and firm.
You should have the dog in less than a week.