The best option is to have your local animal control come out to you and pick up the dog. Many people call the police/animal control when they lose their animal and the animal control people could have a record of who lost the dog to get the dog back to the owner. If you do not want to have them come to you, yes you can bring the dog to the shelter. Make sure you leave the dog in the car with a family member or have them walk the dog around outside while you go inside to tell them you found a stray. This way you lower the risk of a fight in the lobby. There is no charge to drop a stray off at the shelter.
Yeah don't give them to these people. They take them and adopt them off, even with full knowledge of them having an owner.
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