The hospital stay for c-section moms is typically three or four days now not much longer than with a vaginal delivery. If your c-section is a planned one, you can expect to have epidural or spinal anesthesia for the procedure. This is handy, because one of the benefits of epidural anesthesia is that it can stay in place for half a day to a day and morphine can easily be added to provide pain relief in the immediate postpartum period.
Women who had a crash c-section and required a general anesthetic do not have this benefit, but they will still be given pain relief. After a day or so, you will be given oral pain killers, which you can take as needed (and permitted). You will be monitored carefully for the first few days. Most c-section moms are up and about a day after their c-section, just to get to the bathroom and a short walk.
The incision site will likely be painful for quite a while, you will feel abdominal pressure, and might feel groggy after the operation. Once you are home, recovery won't have ended. Your doctor will set you up with a postpartum checkup, and you will need to rest as much as possible after birth. Don't lift anything heavier than your baby and follow your doctor's advice.