I had this and had a laproscopic operation to remove the cyst.
It was simple. The doc made three incisions: one for the laproscopy and two to inflate my abdomin. They have to inflate the abdomin to get the scope in.
BTW, do read up on these cysts. Rarely are they cancer. They will do an ultrasound to look at it (if they haven't already) then a cancer screening to make sure that is clear and then decide if it needs out. Which it sounds like yours does. I also had my ovary removed. Once the cyst was gone and I was recovered from the incision pain, I couldn't believe the pain I had endured for a few years (in my gut, below my ribs, above my belly button) was gone. Just like that. Like a bruise cleared up. It made quality of life much better to be pain free.
Recovery is about a week for the incisions.
You'll be fine. Just ask lots of questions and make sure you have someone to drive you to the hospital; it is outpatient.
Good luck-keep us posted.