how do you know what year a bank note was produced?

Answer 1

What country?
For the USA, one can only narrow it down to what years that the Secretary of the Treasury and Treasurer of the United States whose signatures appear on the note were in office. The Series year isn't an accurate indication.
For example, Series 2003A / 2004A was printed in 2005 and 2006. Series 2006 banknotes are presently being produced - There is no Series 2007.

Here are links to a listing of Treasurers of the United States and Secretaries of the Treasury, including dates when they were in office.

http://www.treas.gov/education/history/treasurers/
http://en.wikipedia.org/wiki/United_States_Secretary_of_the_Treasury

Just for fun, here is a link to the bureau of Engraving and Printing web site, so you can see how many of which series banknotes have been produced over the last four years:

http://www.uscurrencyauctions.com/BEP_Monthly_Production_Reports.htm

Canada and Indonesia put what year the banknote was printed in microprinting on each banknote, starting with the current banknote series.