Caring for an orphaned kitten is a lot of work. Kittens need to stay with their mother for at least 8 weeks to learn proper social skills and behavior. It is safe to take kittens from their mother at 5-6 weeks old, but this is not healthy for them. When rescuing kittens from a feral mother, sometimes it is best to take the kittens away at 4 weeks old to ensure they learn to bond with humans. Kittens learn how to be a cat from their mother, so a surrogate mom will have some big paws to fill.
When left with their mother, newborn kittens normally nurse every hour or two. All day and all night, around the clock. Going longer in between feedings can cause their blood sugar to drop dangerously low, so if you cannot handle this sort of rigorous schedule, you may want to find a rescue group than can take care of your orphans. Young kittens are fragile, and orphans are even more vulnerable to disease and infection. Even with the best care they may not all survive without their mother. It is important not to blame yourself if you lose a baby kitten.
Newborn kittens need to be kept in an environment that is 88-92 degrees. Normally they would snuggle together in a pile with their mother and siblings to keep warm. Inside your clothing is a very nice place for a baby kitten to be, especially if you have only one orphan. They appreciate being under your shirt or even in your bra if you wear one. At about 5 weeks old, kittens can usually tolerate regular room temperatures, until then they would like to be kept nice and toasty. If you use a heating pad under your kitten bed, make sure the babies can move off of it if they get too hot.
As an added bonus, snuggling is good for their social development, and a newborn needs to be held for a minimum of three hours a day to develop properly. The more holding and cuddling, the better. Fortunately, kittens are adorable, and it is usually harder to stop cuddling them. Hold that baby as much as you can, and enjoy it. Orphaned newborn kittens that are held extensively tend to have a better chance of surviving.
An orphaned baby kitten should see a veterinarian right away. Kittens can become dehydrated very quickly, and the baby may need extra fluids under its skin to help it recover. A veterinarian can also help you find the right formula for your kitten and get you started feeding it with a bottle or eyedropper. Be careful not to force food down a kitten, you could get fluid in its lungs and cause pneumonia. Don't hold a baby kitten on its back while feeding it, let it rest on its belly like it would if it were nursing. After feeding the kitten, you'll want to burp it by holding it against your shoulder and patting gently, just like a human baby.
Newborn kittens cannot poop or pee by themselves, they need their mother to stimulate elimination by licking them. You can simulate this by massaging them slowly with a tissue or paper towel until they go. You can also hold the kitten and sort of bounce them on the towel until they eliminate, but do it gently. Kittens chafe easily. They will need to be pottied like this before and after feeding until they begin going on their own, at around 3 or 4 weeks old.
Kittens are terribly messy, but their mother usually keeps everything nice and clean. Without their mother you'll have to groom them yourself. Use a damp washcloth that is not too wet to wipe them down after a feeding, this simulates their mother licking them and keeps the formula from irritating their delicate skin.