On one sidewall or the other there'll be some D O T letters, followed by a number -- usually heat embossed into the tire. The number will end with four digits that are the date code (have been since year 2000)/ The first two digits are the week (of the year) of manufacture, the second two are the last two of the year number. That is, for instance, 0800 would indicate the tire was made the eighth week of year 2000. 4107 would mean the forty-first week of 2007.
Got it?