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.
Empty the Bladder
Newborns cannot evacuate their bowel or bladder unassisted. The kitten you have found may be in excruciating pain or in danger of going toxic from having to retain its own body waste. You should help the kitten at least empty its bladder before proceeding with warming or feeding or even the trip to the veterinarian. With the kitten on a towel in your lap, lightly rub the kitten's body with a rough, dry washcloth. (At that point, the kitten may roll over or otherwise present its bottom to you.) With a generous handful of soft tissue (also to be kept handy at all times) gently stroke the kitten's behind, keeping the tissue in contact. The kitten should oblige by urinating a rather amazing amount. Simply rotate the tissue until kitten stops urinating or the tissue is soaked, whichever comes first. (Did I mention to keep a waste bag handy for this procedure?)
Another method to stimulate evacuation is to use a tissue or wash cloth moistened with warm water instead of a dry cloth or to apply a moistened Q-tip (hold the kitten over a sink or a folded towel if you use the latter method).
Warm the kitten
A newborn kitten is not capable of generating or maintaining body warmth and must depend on its mother (and now you) to sustain warmth and life. Keeping a newborn orphan warm (even on a warm day) is a priority, more important initially than feeding (do NOT feed a chilled kitten, by the way -- you will kill it). Bundling up the kitten will do no good; it has no body heat of its own to retain. And putting the kitten near a space heater or other heating element is neither sufficient for the long-term nor safe. Wrap a heating pad, set on low, in a towel or flannel and place it in or beneath the nesting box, leaving room for the kitten to crawl off the heated area as needed. (Emergency, short-term measures: If you don't have a heating pad, put the kitten on a wrapped hot water bottle or snugged against a tightly sealed and well stabilized jar of warm water. Better yet, put the kitten next to your body -- next to the skin if possible. Then go out and borrow or buy that heating pad after the first feeding or take the kitten to the vet immediately if its condition is poor or questionable.)
Newborns should be shielded from direct light and contained in their den until they are at least three weeks old. Remember to try to provide the kitten an area in the den where it can crawl off the heating pad if it gets overheated. A small airline-style carrier doubles very well as a den and a taxi, though the kitten will soon outgrow it. A pair of large nested boxes is a good den, as long as the kitten cannot crawl out. If you are fostering a single kitten, provide a surrogate sibling in the form of a small stuffed toy or bundled sock.