A few years ago, while living in New York, I was driving home from my life guarding job in the summer and I saw a dog in the middle of a busy (though residential) street.  I turned onto a side street and grabbed some treats and a leash from the back of my car (because, you know I always have those in my car for situations like this).  I crouched down and coaxed the black-lab mix to me (luckily she was friendly and sauntered out of the middle of the road with no problems).  She had a collar with tags on it so I called the number on the tag and no one answered.  I left a message and decided to walk up the road near where I found her.  I saw a few people and asked if they recognized the dog and no one did.  One very friendly neighbor offered to get a phone book so I could look up the name on the tag and maybe find an address.  We didn’t find the exact full-name but someone with the same last name just a few blocks over.
She easily jumped in my car and we drove to that house… I knocked on the door and a neighbor was outside and said that they didn’t have a dog and she didn’t recognize the pup I had found.  I went back over to where I initially found her and saw the mail carrier and figured he probably knows all the dogs in the neighborhood (LOL!).  He didn’t recognize her either.  Now, by this point I had called the number on the tag probably 3 or 4 times. After an hour of searching I had to get home to let MY dogs out to potty after working all day.  I wasn’t sure how she was with other dogs and knowing Shayne’s concern about other dogs, I knew I couldn’t bring her home (it was 95 degrees out so I couldn’t leave her in my car).  So, I called the number one more time and left the person a message that I had to drop the pup off at a local shelter.  I was on my way when I FINALLY got a call from the owner.  He said that his mom was dog sitting while he was out of town.  He gave me the address and I drove back to right near where I found the dog in the first place and returned the dog to a stressed out woman who had no idea how the pup got out of her 6ft privacy fence back yard.  Although I didn’t know it, she was desperately looking for the pup.
Wow, that was a LONG story.  The point is that there are some things you should do (if you can) and some things you shouldn’t  do if you find a dog.  It seems like common sense but apparently not since I’ve heard some “horror stories” regarding lost/found dogs.

Do:

Try and corral the dog by coaxing him/her to you.  You may need to toss treats and gradually get them closer and closer to you.  Turning sideways and kneeling down can make you seem more approachable.  It may take a bit of time to gain their trust, but leashing them will prevent the dog from running away again.

Do:

Check for ID on the collar (if the dog has one).  Call the phone number available on the number and leave messages if they do not answer–be sure to include your phone number and any pertinent information.  If they have a rabies tag on their collar you can contact the vet to get contact information for the owner.

Do:

If safe to do so, try to go by foot in the area where you found the dog… see if anyone recognizes the dog or knows of someone looking for a dog.  Check for any “lost” posters locally while you walk around.

Do:

Call local shelters and veterinary hospitals to see if anyone is aware of a missing dog that fits the description of the dog you found.  Also check websites like Craigslist, Kijiji, or other local places that list lost/found animals.  If you can, post about the dog you found including a picture.  If you couldn’t keep the dog for any amount of time, I would still do these things after surrendering the dog to a shelter.

Do:

Take the dog to a vet or shelter to have it scanned for a microchip or other identifiable bits of information.

Do:

If you cannot keep the pup for any length of time (even a few hours to wait for a returned phone call or to check websites like Craigslist), take the dog to a shelter.  If there is a phone number on the collar be sure to leave a message for the person telling them what shelter you dropped their pet off at.

Don’t:

Chase a lost and fearful dog.  If the dog cannot be coaxed to you, take a note of the time and place you saw the dog so you can give details later.  The last thing you want to do is chase the dog away.

Don’t:

Assume that no one is looking for the dog and keep it as your own forever and ever.  Even if you think the dog is a stray and hasn’t been cared for, there is chance that the dog has been lost for some time and is not in the best shape.

Don’t:

Just assume that someone else will do something… even if you can’t personally get the dog, or stop the dog, or anything… take a note of the time and place you saw the stray and check out local “lost” adverts, post a found/sighting notice, and notify the animal shelters/vets to see if they know of anyone missing a dog.

Don’t:

If you can at all avoid it, please don’t take the dog out of the area where you found it (out of the area as in another state or hours away).  It is much harder to reunite owner and dog if they are not longer in the same area.  If you do ultimately take it out of the area, be sure to contact vets/rescues/shelters/police in the area where the dog was taken from… there’s a good chance the owners live locally and if they are looking for their dog they will rely on alerting local authorities, not authorities in the state where the dog ends up.

Don’t:

Rehome the dog without confirming the dog does not have a microchip and without a sufficient search for the rightful owners.  If you cannot keep the dog long enough to thoroughly search for owners, try checking with a local rescue who may have resources available to help look for the owners (or sufficiently advertise the found dog) or take the pup to a shelter.
 
I want you to think about your pup for a moment… your loving companion.  Imagine that he/she got loose, startled and backed out of a collar, got confused while on an off-leash hike etc.  What would you want the person who found him/her to do?  Those are the things you should do for a dog you find.  What would you definitely NOT want a person to do if they found your dog…. then you probably shouldn’t do that.