If you have a totally smooth vaginal birth, you're likely to head home within 24 to 48 hours of delivery. You'll have to rest a bit after pushing out baby and wait for any anesthesia to wear off, and your doc may want to monitor you and baby for the first day or so to make sure no problems develop. Then, if all is well, you're likely to be back in your pad in no time.
Keep in mind that you may need to stick around for awhile if you have a cesarean or any complications. Use your extra time in the hospital to take advantage of the available support, like breastfeeding and baby care classes.
American College of Obstetrics and Gynecologists. Your pregnancy and birth. 4th ed. Washington, DC: ACOG; 2005.