Help, My Dog is Lost!
Take a deep breath. Check the house and the yard. If you are sure your pet is missing, get out immediately and check the neighborhood. There is a pet tracker locally who recommends calling him within an hour. The sooner you start your search the better. Call Animal Control and advise them that your pet is missing. If they pick the animal up as a stray, they can match the description to your missing pet. GO TO THE POUND EVERY DAY! Your description of your pet may not sound the same as what he looks like if he gets picked up. Collars and tags are great, microchips are better, none are 100%.
He's still missing
If after the first few hours your pet hasn't turned up, you need to cast your net wider. Make up a COLOR flyer with a recent picture of your pet. Use the word "Reward" in big letters. Make as many copies as you can afford and put them up anywhere people can see them; gas stations, supermarket bulletin boards, restaurants, etc. Call local vets and humane societies, post pictures on Facebook and Twitter, send e-mails, whatever you can think of to get the word out. For cats, food-baited traps with something that smells like you may be a good option. For dogs, having people out calling (if your dog is people-friendly) is a good way to go.
Have your pet spayed or neutered. Looking for love is the most common reason to run, 70% of the animals found hit on the road are un-neutered males. If you have a fenced yard, check it frequently for any potential escape points. When traveling with your pet, take extra care. Yes, your cat hates the carrier, but she'll be safe in it. A harness is much less likely to be wriggled out of than a collar. Animals in strange environments behave differently than they do at home. If you know your pet is an escape artist, put some extra safeguards in place like an extra clip on the gate lock. Make sure you have an up to date picture of your pet. An ID tag with your cell phone number is worth its weight in gold. A microchip can mean the difference between your pet coming home or not.