How do I find out when my car was manufactured

It's all in the VIN.

A car’s vehicle identification number (VIN) is the automotive equivalent of
human "DNA".

How to read a VIN
1st character- Identifies the country in which the vehicle was manufactured.
For example: U.S.A.(1or 4), Canada(2), Mexico(3), Japan(J), Korea(K), England(S), Germany(W), Italy(Z)
2nd character- Identifies the manufacturer. For example; Audi(A),
BMW(B), Buick(4), Cadillac(6), Chevrolet(1), Chrysler(C), Dodge(B),
Ford(F), GM Canada(7), General Motors(G), Honda(H), Jaquar(A), Lincoln(L), Mercedes Benz(D), Mercury(M), Nissan(N), Oldsmobile(3), Pontiac(2or5), Plymouth(P), Saturn(8), Toyota(T), VW(V), Volvo(V).
3rd character- Identifies vehicle type or manufacturing division.
4th to 8th characters- VDS - Vehicle Descriptor Section. These 5 characters occupy positions 4 through 8 of the VIN and may be used by the manufacturer to identify attributes of the vehicle. Identifies vehicle features such as body style, engine type, model, series, etc.
9th Character - The check digit "character or digit 9" in the sequence of a vehicle identification number (VIN) built beginning with model year 1981 (when the 17 character digit format was established) can best be described as identifying the VIN accuracy.
A check digit shall be part of each vin (since 1981) and shall appear in position
nine (9) of the VIN on the vehicle and on any transfer documents containing
the vin prepared by the manufacturer to be given to the first owner for purposes
other than resale. Thus, the vins of any two vehicles manufactured within a 30
year period shall not be identical. The check digit means a single number or letter
"x" used to verify the accuracy of the transcription of the vehicle identification
number.
After all other characters in the VIN have been determined by the manufacturer
the check digit is calculated by carrying out a mathematical computation
specified. This is based on vin position, sample vin, assigned value code,
weight factor and multiply assigned value times weight factors. The values are added and the total is divided by 11. The remainder is the check digit number.
The correct numeric remainder - zero through nine (0-9) will appear.
However, if the remainder is 10 the letter "X" is used to designate the check
digit value/number.
10th character- Identifies the model year. For example: 1988(J), 1989(K), 1990(L), 1991(M), 1992(N), 1993(P), 1994(R), 1995(S), 1996(T),
1997(V), 1998(W), 1999(X), 2000(Y)------2001(1), 2002(2), 2003(3)
11th character- Identifies the assembly plant for the vehicle.
12th to 17th characters- VIS - Vehicle Identifier Section. The last 8 characters of the VIN are used for the identification a of specific vehicle. The last four characters shall always be numeric. Identifies the sequence of the vehicle for production as it rolled off the manufacturers assembly line.