It happened to me, just last week. One day I let my cat out the back door in the morning and he never came back. He was missing without a clue for four and a half days. My wife and I were heartbroken. I gave her this kitty on our first Valentine's Day as a married couple. He's been an integral part of our family for the past four years.
Here's are the five steps we took to find our kitty which you should follow at a minimum:
1. Post a LOST ad on your city's Craigslist.com page under both "lost & found" AND "pets". Volunteers for some animal shelters check Craigslist regularly to hopefully match found animals with their owners. Include a photo, description, and phone number. You may consider adding your address or cross streets. In our case, an animal shelter volunteer saw my ad on Craigslist and contacted someone at the shelter who in turn contacted me.
2. Create a flier with the same information. Make tons of copies (I made 120). Tape a flier on every door within 3-4 city blocks. Include telephone poles, light poles, below stop signs, etc. As you do this, talk to everyone personally that you see. Tell them your story and hand them a flier. People who make personal contact with your plight tend to go the extra mile to help out.
3. Visit the local pound / animal shelter daily. Calling is a waste of time. In my case, one lady checked Mr. Kitty in on Thursday and another lady answered the phone when we called on Friday. She had no idea about our cat and told us she hadn't seen him. We could have had him the next day if we had gone to the shelter in person.
4. Check Craigslist, Petfinder.com, and your local newspaper ads online to check for a) anyone announcing that they've found your pet or b) anyone trying to sell or give away your pet. Some people might try to find a good home for your pet if they think it's a stray. They also might try to make a profit if your pet is an expensive or rare breed.
5. Pray. It works. Don't be afraid to ask God for what you really want. You won't always get everything, but he gives more when you ask than when you don't. "You have not because you ask not."
Best wishes to you and yours.