Part numbers are the holy grail of selling these old parts. Without it, a part usually ends up in the swap meet pile. Many older NORS replacement parts may have the part number, but without the manufacturer catalog, there is no way to tell what it fits.
That said, Ford has employed a very logical and easy to follow part number system for most of its existence. It consists of a 2-3 digit prefix which gives the year and model, a center portion which is a basic part number, and a suffix which tells which version of a given part. The nice part about Ford's part numbers is the basic part number rarely changes, meaning a bumper for a Model B will have the same part number as a bumper for a 1977 LTD.
A lot has been written, and is readily available on the net, so there is no reason for me to go into great detail. I always have this page open when researching parts, ad I have found it to be the most helpful.
Many thanks to the folks at Fordification for putting this together.