Instructions
Coax the cat inside by feeding or trapping. Humane traps are available if you can't get the cat contained on your own.
Contain the feral cat. The ideal enclosure would be an outdoor pen, but if you have limited space, experts recommend keeping the cat caged for a time, until you have established a relationship or set up other alternatives.
Set up feeding schedules. Feeding the cat often will earn you trust; experts say feral cats also respond well to calm music on a radio at a low volume. Gradually introduce yourself to the feral cat; don't rush to be friends, as the animal will likely be frightened and on edge.
When possible, take the cat to a veterinarian. The vet will test your cat for feline diseases, give vaccinations and spay or neuter it. This will cost money, maybe a good bit, but these steps are important, regardless of whether you will be keeping the cat or not. Giving the stray preventative care (neutering/spaying) saves dozens of future cats from lives of poverty and danger.
Experiment over time with letting the cat have more freedom. Watch it closely to see if you are successful in "socializing" with the cat; if so, you can keep it as a pet, if not, it may need to be released back into the wild or given to a farm or other outdoor environment.
How to Take in a Feral Cat
Bringing a "feral" or wild cat into your life is a good deed. Left to their own devices, feral cats reproduce and become a burden to the community. Cats in the street are dangerous, not just to themselves, but to drivers and children. With a little care,a feral cat can often be "tamed" to an extent, but it's not always a quick process; for an animal accustomed to helping itself, being taken in is a major transition.