Go back to where you lost sight of your dog, leave your scent there, tell rangers and hang posters at the trailheads and roads.
The short answer
If your dog gets lost in the woods, go back to the spot where you last saw it, stay there for a while and leave something with your scent, such as a worn shirt or your dog’s bed. Tell the ranger or land manager, animal control in that county, and everyone you meet on the trail. Hang posters at trailheads, parking areas and nearby roads, since a dog is more likely to be spotted at the edges, where the people are. Do not bring a crowd to shout through the trees. A calm owner at the last-seen point is more useful than a large search party.
Stay near the point you lost it
Lost-dog groups report that dogs often head back to where they last saw you, or to the car. Wait at that spot for as long as is safe, and then go back to the trailhead. If you have to leave, put your scent item on the ground there, along with a bowl of water. Advice differs on what comes next: some lost-dog groups suggest keeping your scent in one place, while others lay a scent trail, and no study settles it. Note the exact spot on your phone and drop a pin so you can come back to it. Take a photo of the area as well.
Tell the people who run the land
Find out who manages the land: a state or national park, a forest service office, a county parks department, a hunting club or a private owner. Call them, and give them the date, time, last-seen location and a photo. Ask them to tell rangers and staff. Then call animal control for the county where you lost the dog, not only your home county, and ask for nearby shelters. Ask whether any hunting is going on nearby, and tell anyone using the land. Leave your phone number at any visitor center, gate or kiosk.
Put posters where the woods meet people
Your dog may be hard to find in the trees, but it may be seen at the edges. Put posters at each trailhead, parking lot, campground, boat ramp and road crossing. Ask at gas stations, general stores and farm stands near the entrances. Knock on the doors of any homes that back onto the woods, and ask farmers and landowners to check barns and sheds. Protect the paper from rain, since these spots are exposed. If you are far from home, leave a local contact number as well as your own in case your phone has no signal.
Search quietly, in small numbers
Practitioners disagree on how much help to take in, but there is general agreement that big, noisy groups can push a frightened dog further. A few people walking slowly with one who knows the dog is better than twenty calling at once. Stick to the trails and old roads your dog would follow, and check streams, since animals need water. Walk in pairs, tell someone your route and carry water and a light. Do not go in after dark on your own. Keep your own safety ahead of the search, because one lost person makes everything harder.
Set up a feeding station
If your dog does not come back the first day, set up a food and water station where it was last seen or spotted. Use strong-smelling food and put it out at the same time each day, along with your scent item. Add a trail camera if you can, since it can show you whether your dog is the one eating. Expect raccoons and other wildlife, and do not leave food where it will cause conflict with local rules. Ask the land manager first. If you are working with a professional trapper, ask them before you change anything about the feeding.
When your dog appears
It may not act like your dog. A frightened dog can run from its own family. If you see it, do not chase, run toward it or shout. Sit or crouch sideways, look away, drop some food and let it come to you. If it goes off, note the time and direction and come back later. Tell anyone helping to report sightings without following. If the dog keeps visiting one place but will not approach, ask your shelter or a local lost dog group about using a humane trap, since many have people who do this.
Check the dog’s health when you get it back
A dog that has spent nights in the woods may be cut, tick-covered, thirsty or exhausted. Take it to a vet soon, and tell the vet how long it was missing and where. Do not assume it is fine because it is wagging its tail. Keep it on a leash for a while, because a dog that has run once can bolt again.
Sources
Advice on feeding stations and scent comes from lost-pet groups and practitioners rather than studies, so treat it as experience, not proof. See Santa Barbara Independent, How to Find Your Lost Dog: independent.com/?p=625031.