My Cockatiel laid four eggs and one of them hatched. Its been more than 12 hours but she never tried to feed the day old chick and simply warms the baby and sits on three of her other eggs. Has she abandoned it clearly? If so, how do I take care of it?
It is still too early to panic, so be calm but be prepared. I've often had cockatiels who did not attempt to feed their babies for the first 24 hours. The babies usually still have some yolk sac remaining and will be fine, as long as the parents are keeping them warm. If there's no feeding after 24 hours, then you may need to help.
First, you need some high-quality bird baby food. (I have had excellent results with LaFeber's Nutri-Start.) Do not waste your money on low-cost baby food unless there's nothing else available. Then, follow the instructions on the package carefully. Food should be very watery for young chicks. Food temperature should be about 104 degrees Fahrenheit (cockatiel body temperature). You can use a syringe or eye-dropper to feed the baby, or use a 1/4 teaspoon steel measuring spoon bent in at the ends (so that it resembles a parent cockatiel's bill--I've had great success with this, but it's messy, and you'll need to clean the baby with a tissue after each feeding). The baby should not be over-fed. The baby's crop should be tense but have a little bit of give (almost exactly like the feel of a tennis ball) after feeding.
A very good source for guidance on feeding methods is: http://www.cockatiel.com/handfeeding.html
Best wishes--I'm sure that you'll do fine.