There are generally two methods of anesthesia for cesarean delivery.  

Regional - No pain below the chest so that surgery can be performed without pain being felt

General anesthesia - You go sleep for the duration of the procedure. 

The first method is preferable as you can be awake and participate (see the baby through a clear clean drape or screen) in the delivery of the baby. 

Regional Anesthesia - Spinal, Epidural, or Combined Spinal Epidural Anesthesia