Serial Numbers
Bicycles (except children's bicycles) are almost always required to have a frame or serial number. Many manufacturers use a date-code as part of the serial number.
For example, a Brompton uses YYMMXXX as their serial code, so a Brompton with a serial number of 1306123456 was manufactured in 2013.06 or June 2013
However, many other bicycle manufacturers don't use date codes and so you can't easily decode it. Some of these manufacturers will provide their own serial number lookups on their websites. Some of the other ones have been reverse-engineered by their rider communities. The best way to find out is to google "manufacturername bicycle serial number date of manufacturer."