Determine what kind of Deluxe Reverb amplifier you have, a Blackface or a Silverface. This is the easiest part of the process: If the front of the amplifier is silver in color, it's a Silverface; if black, it's a Blackface. Blackfaces were produced between 1963 and 1967; Silverfaces between 1967 and 1976. This will narrow the range of possible manufacture dates considerably.
Locate the serial number on the Deluxe Reverb amplifier. Regardless of the year of manufacture, the serial number will be located on the chassis -- the metal plate that holds the transformer and tube rack in place in the back compartment of the amplifier. When looking at the back of the amplifier, the chassis will be readily visible at the top. There will be a box labeled "Serial Number."
Determine what year the amplifier was manufactured by analyzing the serial number. All vintage Deluxe Reverb amplifiers's serial numbers will begin with the letter "A" followed by a sequence of six numbers. The numbers are sequential across models. For example, the first Blackface Deluxe Reverbs will have numbers between 00100 and 00300 -- these were produced in 1963. See References for a link with a comprehensive list of the number sequences and their associated years of manufacture.