Where on an old Fuji Supreme would i find a stamping on the frame which indicates its size? I've been looking all over and found the serial number but nothing that denotes the frame size. How would I measure it?

Most bikes are measured from the centerline of the bottom bracket to the top of the top tube.

To the top of the seat tube you mean? But that's not a hard and fast rule. Some manufacturers measure differently, according to Sheldon Brown https://www.sheldonbrown.com/frame-sizing.html

The size may be encoded in the serial number, but I have no idea how to interpret it...you might try contacting the manufacturer.

If the number is just for trivia, measure it like Retro says.

If you're selling the bike, measure it and say where you measured at.
If the manufacturer uses some odd measuring point, and you don't know it and your purchaser does, then you've given him all the information you really can and he should be knowledgeable enough to deduce the 'correct" size.
If the manufacturer uses some odd measuring point, and neither you nor the purchaser knows that, then it doesn't matter.

From the Sheldon Brown site:
"Bottom line: seat tube "frame size" numbers are nearly meaningless unless you know how they are measured!" So measure it and say how you measured it and there you go.