The answers come from
Anesthesia & You... Anesthesia for Ambulatory Surgery, an informational document prepared by the American Society of Anesthesiologists through the cooperative efforts of the Society's Committees on Communications and the Committee on Ambulatory Surgical Care.

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What can I expect after the operation until I go home?
After surgery, you will be taken to the postanesthesia care unit, often called the recovery room. Your anesthesiologist will direct the monitoring and medications needed for your safe recovery. For about the first 30 minutes, you will be watched closely by specially trained nurses. During this period, you may be given extra oxygen and your breathing and heart functions will be observed closely.

In some facilities, you may then be moved to another area where you will continue to recover and family or friends may be allowed to be with you. Here you will be offered something to drink and you will be assisted in getting up.