What is the indication for the surgery?
With an experienced surgeon, you should do fine. The risks vary with the reason for the surgery, and you and your doctor should discuss these until you are comfortable with the procedure.
You can expect some soreness. The surgeon may inject some local anesthetic into the incisions at the time of surgery. When that wears off, oral pain meds are usually sufficient. When I had my gallbladder removed, I did not use anything stronger than ibuprofen after the day of surgery.
You may have some pain over the top of your shoulder. This is due to residual bubbles of the gas used to inflate the abdomen in order to see the internal organs. The gas gets under the diaphragm when you sit up. Irritation of the diaphragm causes pain you feel in your shoulder. Lying down usually makes the pain go away by allowing the bubbles to move away. The gas is absorbed in a day or two and the pain goes away.
If you are premenopausal, you can expect some symptoms of estrogen deficiency almost immediately. You should discuss with your doctor how you plan to deal with them.