I had a lap to remove a chocolate cyst (called an endometrioma). How long you are under varies depending on what they do in there, for a cyst only, it would likely be pretty short - perhaps as little as 30 mins?
You wake within a very short time of anaethetic drugs stopping, but you are not really alert for a good while after - I am a very slow waker and took ages after my last op (the lap and endo/cyst removal).
For just a cyst I imagine it would be day stay only, so usually once awake and probably not until you've eaten and done a wee, you'll get to go home.
Expect shoulder tip pain from the gas used to inflate your abdomen trying to escape, heat packs help this. Also expect to be quite tender at the incision sites - I had a week off work and was tender for about 3 days - but I also had alot of endo removed as well.

Tests of samples taken during surgery are fairly run of the mill procedure. Please try not to worry, the vast majority of cysts are benign.


ETA regarding pain meds. I found that nothing more serious than panadol was needed after I came home (I had an overnight stay so had stronger meds in hospital).Anything removed is done by burning so it actually seals off the nerve endings and no pain is felt inside.