Here is our little "wild kitten" Sassy.
Her mom is a feral cat that has been in the community (we live in the country) for a couple years. She brought Sassy and 3 siblings around to a safe place under one of our decks about a week before Thanksgiving - right before our week of minus 20 temps. The kittens were about 4 weeks old then and we fed them all and kept them warm - outside - with a little shelter and an outdoor pet heating pad that Bob put together with the help of the pet stores.
We did that for about three weeks as we tried to interact but there was no catching them. The momma was very skittish as one would expect. We finally captured all but this one and took them to our local animal shelter, Heart of the Valley. They make sure they are healthy, spay or neuter as needed, give shots, chip them and then put them up for adoption. The momma, being feral, would be adopted as a barn cat and they wave the adoption fee for her.
This one was not about to be caught, but we finally succeeded about a week later. We socialized her for a few days inside in a kennel and then we just fell in love with her and decided we wanted to keep her so we have. And she has become a wonderful member of our household.
This morning was her first trip to the vet and she is healthy and about 11 or 12 weeks old now.