You need to make your hidden folders visible. Go to control panel, folder options, view tab, select "Show hidden files and folders".
The saves are in either C:\Documents and settings\[user name]\Application data\UFOAI (for Windows XP) or C:\Userdata\[user name]\UFOAI or similar in Windows Vista or 7 (not quite sure of the path there).
Not that it will do you much good, since one of the updates within the next week or so will make savegames incompatible with the newer revisions.