Answer:
The following answer is graphic and descriptive.
In humans, the female becomes pregnant when her egg is fertilized by a man's sperm. The fertilized egg implants itself (attaches to) into the uterine wall. The uterus is also called "the womb"; it is an organ in the woman's lower belly. The uterus is mostly made of smooth muscle tissue and it has a very good blood supply. When the egg implants, the attached portion grows and becomes an umbilical cord - this cord goes from the baby's belly to the mother's uterus, and this cord brings all the nutrients from the mother to the baby through the mother's bloodstream. Blood vessels are in the cord. While in the uterus, the fetus is in a special fluid called amniotic fluid. The uterus would look like a balloon filled with water-- but amniotic fluid is not just water; instead it has special nutrients the fetus needs to live.
The fertilized egg quickly begins to divide (cell division) until millions and millions of cells are formed. Each type of cell creates a certain part of the baby's body; for example, bone cells make bones; muscle cells make muscles. While inside the mother's womb, these dividing cells and forming baby is called a fetus. (Doctors don't use the word "baby" until after the baby is born.) The fetus continues to grow inside the uterus for about 9 months (on average). Nine months is about 38 weeks. This period of time is called a "pregnancy".
A baby, though, can be born at different times. If born very early, it may not survive. If born later, it has a better chance to live. Most often, a fetus has no problems and waits until between 7 and 9 months (or more) to be born. If a pregnancy goes more than 8 months (38 weeks), a doctor will induce labor by 40 weeks.
The process of "being born" starts many weeks before the baby actually is born. Hormones in the mother change. The baby starts to move downward, and most babies have to "turn around" in the uterus first. During pregnancy, the baby lays sideways with it's head on one side or the other, or the head is up (almost under the bottom of the mom's ribs). But to be born, it's best if the baby's head is down so the baby is upside down in its mother. Hormones make the muscles in the uterus contract (get tight) and release so it helps the baby turn and get into the right position. When the baby has turned around upside down, doctors say the baby has "dropped". From the outside, people can notice that the mom's belly is now "fatter" at the bottom and less "fat" or round at the top like it had been for many months.
It can take a couple weeks for the baby to turn upside down. While this happens, the mother may have false contractions. In other words, it kind of feels like labor has started but it hasn't really. These muscle contractions come and go, similar to you making a fist with your hand then opening your hand and relaxing. A mother may feel one contraction... then nothing more for days... then another contraction.... and so on.
Finally, though, the contractions start to get stronger and they don't go away. In fact, the contractions start coming closer and closer together (like as if you made a fist, opened your hand...and a few minutes later, make a fist again). Once contractions start, they can go on for many hours. The longest normal delivery can take around 24 hours (a whole day); if the baby isn't born by then, doctors will do surgery to bring the baby out (by C-Section).
So, when a pregnant mom feels contractions, she usually goes to the hospital when the pains are 2 minutes apart (example, it would be like you made a fist and open it, look at a clock and at 2 minutes and then make a first again). At the hospital, nurses help the mother get ready to go through "Labor and Delivery".
"Labor", like I said, can last a long time. In the first hours, the mom can lay in a bed, sit in a chair, or walk around if she wants. Walking helps to keep moving the baby downward. But... the contraction pains get stronger as time goes by. Then, mothers want to lay in a bed because it is more comfortable.
The "balloon" or sac around the baby must "break" before a baby can be born. If it doesn't break on its own, a doctor uses a special instrument to open the sac. It can happen naturally after contractions start. If it happened naturally, a woman says "my water broke"-- the water didn't really break, but the sac broke and then lets the "water" (the amniotic fluid) come out.
After the "water breaks" (or is broken by a doctor), contractions come harder and more frequently. Labor is painful. Many women decide to have medication to lessen the pain; there are different kinds of medicine but it's too much to describe here. The hours go by with the mother having more contractions and the baby moving closer to being outside.
Finally, the mother feels a great need to "push", just like when you need to have a bowel movement. Except, during labor and delivery, it really hurts to push--- but it also hurts to not push. Every mother at this point just wants it to be over. She just wants the pain to stop and for her baby to be born.
During these hours of labor, nurses and doctors check the mother and baby frequently. Finally, the baby's head "crowns". Crowning means that a nurse / doctor or the baby's daddy can see the top of the baby's head starting to come out. The doctor makes a special incision to give more room for the baby's head to come out. While he makes the incision, the mother should not push.
But after the incision, the mother is strongly instructed to "Push!" Usually it only takes a few hard pushes before a baby is fully born. Some women have to push more than other women.
In a normal birth (normal being "head first"), the head comes out first. The mother then pants instead of pushing so the doctor can help rotate the baby a little in order to make one shoulder come out next. When the baby's head and one shoulder are out, the other shoulder slides out, followed by the baby's body.
A nurse helps by quickly suctioning fluid / mucous out of the baby's nose and mouth. The doctor may swat the baby's behind to make him/her cry, if the baby hasn't cried yet. The "cry" means the baby has taken its first big gulp of air, which is why doctors want the baby to cry. Other doctors might flick the baby on its foot to stir the baby to cry.
Quickly the doctor will first clamp and then cut (or the baby's father is instructed how to cut) the umbilical cord. Cutting the cord does NOT cause the baby or mother any pain. The baby is then put onto a specially warmed bed, wiped dry, weighed and measured, and special ointment is put into both eyes to protect from disease. A nurse or doctor will perform quick tests called an APGAR score; this score tells how well the baby looks medically and how well he/she is responding. For example, if the mom had medications the baby might be sedated (sleepy) and might not cry vigorously, so the APGAR might be a lower score. Doctors re-do the APGAR after 5 minutes.
By then, the baby has been wrapped in a blanket and a knit cap is put on its head to prevent heat loss, and the baby is brought back to its mother to hold or even to breast feed for the first time.
There are many variables, many differences in each baby's birth. What I described above is a birth with no problems or emergencies. Every pregnancy and every "labor and delivery" is different, though. While doctors and nurses follow certain set procedures or ways of doing things for a normal birth (no problems), there are other ways of doing things if a problem happens. Doctors and nurses watch for problems they know could develop and try to prevent the problems from happening. One common problem is the need for surgery called a C-Section.
If you have questions after reading this, please ask your parents or family doctor.