Bleeding probably comes as the biggest surprise for most women. The blood shed after the vaginal or cesarean birth of your baby is called lochia. The lochia will start out bright red and contain clots for the first few days. It is coming from the healing of the placental site as your uterus shrinks back (involutes) it's prepregnancy size, which takes about six weeks. The bleeding will generally become light in flow and lighter in color until it stops completely. This signals that the location where the placenta was located has healed over.
Let your lochia be your guide. If you're doing too much you will generally notice a heavier or darker flow than from the day before. The lochia should smell much like a menstrual period. Any other odors or problems should be reported to your practitioners.
Since your body is healing you will want to use pads to catch the flow rather than tampons. This will also help protect you from infection. Since the first few days are the heaviest, wear older underwear or the mesh panties from the birth to avoid ruining your good clothes. I usually recommend the incontinence pads, or even small baby diapers for these first few days. After that any type of menstrual pad will generally work.