To care for kittens, you don't necessarily need a lot of space. For a newborn kitten, a carrier is enough, and as they grow, you upgrade to a playpen or small room. Just make sure they are safe, comfortable, and warm; and that their space is easy to clean. There are some supplies you can use: to keep them warm, place a comfortably warm heating pad close to the kitten, but leave enough space so they can leave the heating pad if they want. You can also line the area with baby blankets. If they are over three weeks old, don't forget to get a litter box.
Check the article "Fostering" on kittenlady.org for complete and detailed information on how to start fostering.
Photo by Sahand Babali on Unsplash