First off, WHAT SIZE IS THE FRAME??? I've been looking for a 53 pink Schwinn for, well, some time now.
Anyway, your bike should have a small round headbadge. THIS is where you find that four digit serial number where the first three #'s are the day of the year, and the last is the last digit of the year. Now, as for knowing whether it's 76 or 86 (etc.), you usually can just tell by the color/graphics.