After your baby is out, your uterus will continue to contract as it begins to work its way back to normal size. As the uterus shrinks, the placenta becomes detached from the uterine wall and is forced down towards the cervix and out the birth canal. Generally women feel the need to push gently as the placenta is expelled, but most claim it is only mildly uncomfortable.
The placenta may come anywhere from five minutes after the baby to an hour after the baby. As long as you are not experiencing excessive bleeding there is no need for alarm. If you feel you need to encourage the expulsion of the placenta, you can nurse your baby or stimulate your nipples by rubbing them, or you can suck your thumb to stimulate a pressure point in the mouth. Both of these techniques can increase contraction strength and frequency and encourage the placenta to detach and be expelled.
Your uterus will continue to contract for the next several days to weeks. Expect that each time you put your baby to the breast, your body will give you a good contraction. This serves to return the uterus to pre-pregnancy size and close off the site of placenta attachment to prevent bleeding. You should expect to bleed for at least two weeks as your placental "wound" heals and your body returns your uterus to a non-pregnant state. Use this bleeding (called lochia) as a guide to activity. If the flow increases or the blood gets darker, you have been doing too much. You want the flow to decreased and get "pinker" until it stops.