Most often the search will begin at home. For cats, it is important to search in and around the house: in the bushes, under decks. in sheds, anywhere a cat could hide. A frightened cat will not respond to the owner's voice, so the search must be very thorough. A humane trap can be very helpful in recovering a cat who is frightened or hiding.
Dogs are more likely to have traveled away from home, but the search should begin at the place last seen. The dog could be hiding, ill or injured, especially on a large or wooded property. If not found, look for evidence of direction of travel such as paw prints or tufts of fur.
Many neighbors will want to help with your search for a missing pet. Be sure to ask them, if they see your pet, to notify you at once and not try to capture them. Shouting, clapping hands, and chasing will only frighten a pet even more and may cause them to run into traffic.
Ask permission to search neighbors' yards. Check every nook and cranny including vents that lead under the house.
Sometimes a pet will go missing at a veterinary hospital, boarding facility, or other public place. Cats will most often run to the nearest hiding place and hunker down, so searching the immediate area is often successful. Dogs will often run off, but circle back later. This often happens in the case of car accidents where the dog jumps or is thrown from the vehicle.
The owners of missing pets can be distraught and not thinking of themselves and of safety. Search during the day when possible. If searching at night, be aware of your surroundings and bring a companion. Ask permission before going on others' private property, and notify police of your activities if you think someone may be concerned. Be especially careful around roads and highways, or isolated areas. Ask local law enforcement, highway patrol, park rangers, etc. for advice and assistance if you are concerned for your safety.
Remote cameras are helpful to determine if a missing pet is in the area. Sometimes a frightened cat or dog will hide and only come out in the middle of the night to eat or drink. The camera will prove that the pet is nearby and can help you focus your search and recovery techniques. You will want to set up your camera where it will capture the pet's image but not violate anyone's privacy. There is also a risk of the camera being stolen as it is left outside.