On the way to (or at) veterinary clinics: Animals often try to escape in fear from veterinary clinics or during transport. Always take a second person along to manage the pet – transport cats and small dogs in latched carriers (with breathing vents) and never open the carrier during transport. The carrier must be opened only after the clinic doors and windows are secured. If admitting the pet for in-patient treatment, get a guarantee from the veterinarians and staff that the gates will be locked at all times to prevent escapes.
Pedigree dogs are at high risk for theft: Avoid the pet trade if you are looking to get a pet. If you already have a purebred animal, never leave him unattended even for a split second. Get a reputed vet to spay or neuter them so they aren't stolen for breeding.
During walks: Aggression especially during mating season might cause your dog to run away when confronted with a potential threat. While taking him for walks, use a harness instead of a regular leash (wraps around the chest area). Carry a bottle of lukewarm water and splash it on sparring animals to discourage them.
While roaming free: Dogs should never be allowed to roam freely even within the locality and must be taken for regular walks only on leash or harness. Free-roaming dogs are at risk of theft, accidents etc and might run away after hearing loud noises and be unable to find their way back.
Un-tagged dogs: Dogs that don't have their owners' mobile numbers on their collars are at high risk even if they are found, as there is no way to track the owner. Use a double-collar – one that is permanent and another that's attached to the leash for walks – both must have your number engraved on the collar.
Visit this site for searching tips - www.wikihow.com/Find-a-Missing-Pet, and use sites like Facebook to spread the word. Mention a reward for successful rescue, and add that the finder must confine your pet and call you immediately to ensure the pet doesn't disappear again while you're on your way to pick him up.