Watching surgery is fantastic. I may have a little perverse idea of what recreation is, but I shadow in the OR all the time. First off, if you work around surgeons it should be easy. Work hard, get to know them, and then just ask: humbly enthsiastically and confidently. If you don't work around surgeons in a hospital or something, then ask around. Ask another doctor (someone else mentioned this), if they know/like you they should help you. Remember, you're not asking for a pony, you're asking to be a part of a very educational and pertinent and motivating experience. Be persistent, but be understanding if an individual gives you the runaround because some are a little uncomfortable about certain cases, but I've never had someone say "no". Crap I just jinxed myself.
Good ways to ask are:
"I was wondering if there were any cases coming up that would be appropriate to watch?"
"I am pretty interested in seeing a *insert procedure here*, do you think that would be a good one to watch?"
"Do you have any *insert procedure here* coming up?"
"I'm applying to medical school next year and am really interested in surgery, do you think it'd be possible to shadow you for a day in the OR? (or clinic?)"
By the way, they are more interested in you if you say you're premed. Prepare well for the operation by boning up a little on the site anatomy. It helps you to ask intelligent questions if appropriate and understand what's going on.
If anyone has any other questions about observing in surgery let me know. (Sort of a stupid area to have an expertise, but oh well)