Firstly you need to find out if the cat is lost, cats have a habit of visiting homes regularly resulting in people assuming its lost but it may live somewhere close by. Start by putting on a paper collar with your name and number, so if it is owned by someone they can call you to let you know the cat has a home.
Try to get a good photo of the cat and put it on social media pages in your local area, it may have just got lost off of the area he/she lives in, so someone may comes forward to claim him/her.
You can put up posters in the local area and speak to neighbours about the cat, someone may know something, and the owner may be found.
Check on social media sites covering your area that no one is looking for the cat, often someone has posted images of their missing cat.
Call your locals vets and ask if anyone is looking for the cat you have found, and the vets will be able to check to see if the cat has a microchip. If a microchip is found the vet can
get the details and contact the cats owners, if no microchip is found hen the cat will need to be rehomed.
The cat will be taken to a rescue centre, the rescue will health check the cat, get it up to date with microchipping, neutering and vaccinations, then a new home will be found .