This article is from the Care of Orphaned Kittens FAQ, posted to rec.pets.cats newsgroup. Maintained by Sharon Talbert with numerous contributions by others.
Heat the formula (in hot water) until it is comfortably warm. Test a stream on the inside of your wrist, first shaking the bottle to even out the temperature. Within easy reach, set a rough washcloth, paper towel, and a box of tissue. Also keep a cup of hot water nearby (but not where it could tip onto the kitten) to warm the nurser as needed. Then lay an old towel, the fluffier the better, across your lap. Hold the kitten belly-down, steadying and guiding the head to the nipple with the same hand that is holding the bottle. (This is just my technique; you may find another that works best for you.) Try to center the nipple in the kitten's mouth, over the tongue, and apply just enough pressure on the nurser to bead out a bit of formula on the nipple. If this is not enough to induce the kitten to begin suckling, squeeze a tiny bit into its mouth and wait for it to swallow before (gently!) squeezing again. This can be even trickier than it sounds, particularly if the kitten is desperately hungry. Convincing a frenzied kitten to slow down and suckle is no easy task. Another kitten may be put off by the strangeness of the offering and so will resist feeding or may be too weak to take the nipple immediately. Be patient and calm and persistent, applying careful pressure on the nurser to keep the formula coming at a natural rate without squirting it down the kitten's throat. Watch the ears: If they start to bob, the kitten is getting just the right amount of formula. If formula bubbles out the nostrils, pull back immediately -- you are drowning the kitten.
Do not overfeed, especially at the first meal. A series of small meals is better than one large one. And don't go crazy trying to follow the complicated instructions on the formula container. Feed the kitten until it settles down and its tummy is full but not distended, then gently remove the nipple and rub the kitten gently but briskly all over with your hand or that rough dry washcloth. (Remember, you are a momcat now; your baby needs the stimulation provided by that tough-love tongue all mother cats have.) If the kitten doesn't immediately begin to complain and nuzzle for more milk, it is fed. Continue rubbing or patting until you get a burp. If you don't get a burp right away, try putting the kitten over your shoulder like any other baby and patting it gently on the side or back. Then return it to the heating pad for about 15 minutes before going to the next step. (Or to the next kitten, if you are caring for a litter.)
A special note on suckling. The suckling instinct in very strong in these little guys, and they are likely to suckle on another. This behavior can be lethal to a male kitten if the genitals are suckled, causing swelling and impaction of the urinary tract. You may need to separate kittens from one another, or at least separate the aggressive suckler. The single kitten should be provided a surrogate momcat or sibling in the person of a soft plush toy that can be snuggled and suckled. Keep the surrogate "mom" and the kitten's bedding clean but chemical-free, for safe suckling.
Frequency of feedings
Feed a newborn at least every four hours or on demand. Do not overfeed. Be prepared to do night feedings.
A note on tube-feeding. The feeding process can be greatly speeded up by feeding per catheter directly to the stomach. Consult with your veterinarian and insist on a training session before attempting to tube-feed, incorrect insertion of the catheter could flood the kitten's lungs. I do not recommend tube-feeding on a daily basis; kittens need nurturing, physical contact in order to thrive almost as much as they need nourishment. If you do tube-feed, handle the kittens. Put them in a sling or fanny pack and wear them around the house (I use a kitten snuggly made by a friend).