Cats usually give birth to 2-5 kittens. Their exact number can be determined by X-ray, but this is not commonly done. If you are worried about your cat, your vet can do an ultrasound, check the heart sounds, and estimate the number of kittens.
You are sure to notice the beginning of labor. The cat will begin to lick herself around her vulva and may start to groan. If she's giving birth for the first time, she may appear nervous. Her temperature drops below 38 °C, then contractions begin and within an hour, quite soon after the amniotic fluid outflow, the first kitten should be born. Kittens are born about 15 minutes apart, but it may even be an hour, so don't panic.
The cat removes the kittens from the amniotic sac after birth. If she doesn't do so, it's time for you to step in. Very carefully tear the sac and remove the kitten. By licking her kittens the cat not only cleans them, she most importantly stimulates them to start breathing. However, she may be so exhausted or busy giving birth to another kitten that you may have to intervene. Take a towel and gently rub the newborn kitten, simulating a cat's tongue. It is also good to place the kitten nose down so the amniotic fluid drains from its airways.
After the kittens are born, the cat eats the placentas, but you should first count the placentas and make sure the number corresponds to the number of kittens. If a placenta stays in the cat, you should go see the vet, as it could cause an infection.
Another process you need to help the mother with if she can't handle it herself is cutting the umbilical cord. She will usually cut it with her teeth, but if she doesn't, tie a piece of strong thread around the umbilical cord about 2 cm from the kitten's body, and then one more knot 2 cm further. Then all you have to do is cut the cord with sharp scissors between the knots.
When the newborns are clean, they immediately begin looking for their mother's nipples and begin to suckle milk. Don't unnecessarily touch the kittens or cat; let them get used to the new situation and take care of themselves.
If everything goes smoothly, don't panic, give the mother some peace and leave everything to her. Cats often give birth at night, leaving a surprise for you in the morning. You should only seek out a vet if the water broke and the cat has been pushing for a long time but no kittens are coming. Another dangerous situation requiring expert intervention is dark, bloody or foul smelling discharge. If you're not sure, leave the cat and call a vet. After you describe the situation he will either calm you down or instruct you to come to the clinic.
If you are dealing with this now, I wish you strong nerves and good luck.