Blogger Sweephand is one of the leading experts on vintage Citizen's. Illustration from Sweephand:
Quote from Sweephand with my comments in brackets:
The key is knowing which decade the watch was produced in, and the Movement Table is useful for determining that. (The watch above is from the 70s).
The first three numbers in the serial are used for the date – the first number is the year. (Thus the watch above is from "3" = 1973 and "11" = november).
One more example:
This watch is a 51-1811 and has a caliber 8200A movement produced from 1975. The serial is "0" = 1980 and "03" = march.
And one more 51-1811:
This watch is from "8" = 1978 and "08" = august.