First things first walk around your lawn or neighborhood as they could just be hiding under a porch, or in the bushes.

Put out their litter box and maybe some water, I recommend holding off putting out food for a few days as it may attract predators. Try getting a camera of sorts to leave outside to check if your cat is coming back.

Print out fliers to hang over your town, and the border of surrounding towns depending on where you are.

Post and look through PawBoost or other lost pet sites. Try Social Media too, maybe a town Facebook group?

Call your local animal control, and shelters they may have already picked your fur baby up, and if not its good for them to know in case they do.

Visit shelters in person, even if you call. They have a lot of pets coming in and one worker (usually a volunteer) may not know about every single animal nor have the time to check

Get a cat trap, and put it outside with some food in it and wait, make sure to check it every day as your fur baby may be inside...or another animal just looking for a snack.

You could also hire a pet detective, yes they exist and they help you find your lost pets!

Most importantly, never give up hope.

If you spot a cat, do not chase it. Take a photo of him/her (try to get as clear as picture as possible) and take note of the location. Try calling the cat over to you, do not yell. If the cat starts to run off stop and leave it alone

Try using food to lure them over to you, maybe a toy.

If you do not successfully capture the animal post the photo and location on sites like PawBoost or social media. Hopefully the owner will see it and visit the location.

If you do successfully capture the animal put them in a closed location away from other pets you may have as this new friend could have fleas, FIV or other contagious things you don't want to expose your pets to. Always wash your hands before interacting with a different pet.

Give them some water and a liter box, if you don't have a liter box check out my step by step tutorial on how to make one here!

Call animal control to alert them you have found a pet, they should have a microchip scanner, if the animal has a microchip the owners should be fairly easy to locate!

Try calling local vets, they will have a microchip scanner and may even know the animal!

Post on pet finding sites such as PawBoost or try social media.

If all else fails the animal will need a home, you may want to adopt them yourself but if not take them to a local shelter. Please do not try and find a home for the animal yourself as potential owners need to be properly vetted and shelters can do this well.