One stray cat can start a colony quickly. The easiest way to prevent this is to catch the stray and make a trip to the veterinarian to have her sterilized. Then you can keep her as a pet, ask the vet to help rehome her, or place her back where you found her.
Feed the mother cat for a few days before you begin the capture process. A momma cat nursing kittens will appreciate the food, and while you shouldn't expect to tame her in a few days, you can definitely get her used to your presence.
Scoop the kittens up and use them as bait to get the momma kitten into an enclosed space, such as a garage or laundry room. This works best with very young kittens. Don't expect the mom to follow at your footsteps. She will undoubtedly run off, but she will keep her eye on you and want to go after her kittens and bring them back to her preferred location. You need to be patient enough to hang around, far enough back to not intimidate her, and shut her in the room when she goes after her kitten.
Set a trap. If your first attempt doesn't work, you may want to set a humane trap to catch the cat. You can purchase humane traps at most box retailers, or borrow one from a veterinarian or your local animal control office. Use tasty bait, such as canned cat food, to encourage momma to enter the trap.
Check the trap regularly. There are several reasons this is important. The first, of course, it that when momma is in the trap, she is not able to feed and care for her kittens, so you want to reunite them as quickly as possible. The other reason to check frequently is that the trap will attract other animals as well, which could cause problems for momma cat and her kittens. If you accidentally catch a raccoon, opossum or other wild animal, contact your local animal control for advice.
Transfer the mother cat to a travel crate or transport her in the trap. Do not reach into the trap with your bare hands and attempt to scoop her up. She will be stressed and escaping will be the first thing on her mind. If you transfer her to a travel crate, place the kittens in first. If you leave her in the trap, place the kittens nearby in a box so she can keep her eye on them.
Always check with your veterinarian before changing your pet’s diet, medication, or physical activity routines. This information is not a substitute for a vet’s opinion.