How can I find out when my machine (or any Mac) was made?

Welcome to the Apple discussions

You can enter your serial number at http://support.apple.com/specs/#powerbook and it will tell you what specific model Powerbook you have, so at least you can bracket the build date between models. If you have an active Applecare agreement on a system, there may be more detail, however, I think most Applecare's have expired on Powerbooks. Otherwise, I'm not aware of anyplace you can find the build date of your system.

On PowerMacs, PowerBook G4 & iBook G4, hold Command, Option, Shift, Delete keys and Power Button. Hold for a while (5 seconds), fans will kick on & then an audible tone will sound, continue holding all keys down. System will reboot, continue holding keys down. You will get to the "Open Firmware" prompt page (light grey/white with black lettering), it will give you precise info about your Mac. When finished type "mac-boot" and hit enter/return to boot back into Mac OS

Entering your Mac's serial number at this website will give you its year and week of production:

http://www.chipmunk.nl/klantenservice/applemodel.html

Try here: http://www.appleserialnumberinfo.com/Desktop/index.php

In answer to the part of your question about when "any Mac" was made, this site http://www.apple-history.com/?&page=faq will give you all the Macs, their specs and dates.