Disclaimer: I?m not a SAR professional or even a volunteer; the following is based on a bunch of books I read last year in order to teach a ?merit badge? to a group of our cadets. Please do not mistake it for an actual informed opinion (I love offering opinions on things I know nothing about <img src="/images/graemlins/wink.gif" alt="" /> )
Check out
www.nasar.org - but in general I wouldn't wait to notify the authorities if someone were lost. If you go searching on your own (because you don't want to "bother" those nice Search & Rescue people?) and you get lost yourself, then they have two searches to conduct - or perhaps none <img src="/images/graemlins/shocked.gif" alt="" /> In addition, a search organised by people who aren't properly trained may miss important clues, or obliterate them (it will certainly make the tracking dog's job tougher if a bunch of helpful Henry's have been traipsing through the area). Untrained searchers raised on the ?leave no trace? philosophy may unthinkingly pick up a candy wrapper that the subject has dropped without realising they?ve just destroyed a vital clue.
If you've already notified SAR, you're confident that you're adequately equipped to survive and not get lost, and time is of the essence (e.g. she's a non-smoker wearing a cotton halter top and cut-off blue jeans, and the rain is turning to wet snow) then I would stick to the paths. From what I've read on the subject, backpackers and day-trippers tend to stick to a path - at least at first. I'd look for forks in the path where they might have taken a wrong turn.
Don't forget about passive searching, either - build a signal fire and generate a nice column of smoke. Or go fly a kite, if you have one ? something bright and colourful, raised as high as you can get it. Not as effective in dense freezing rain, of course, but it won?t do any harm and might be very effective in good weather.
The National Association for Search and Rescue (NASAR) has more literature on this topic than you?ll likely ever want to read - most of it's not readily available from Amazon or B&N. <img src="/images/graemlins/smile.gif" alt="" />