It's a well-kept secret in the tire industry that a) tires are unsafe after six or seven years, and that b) tires that are sold new are not necessarily new - they may have sat on the shelf for years before being sold to you. They look new, they were sold "as new" - but they are not new.
Fortunately, there is a very simple way to find out the actual age of the tire, starting from its manufacture. Stamped into the side of every tire is a date code, that indicates the actual date of manufacture. It looks something like this:

In this case, it's the number "4209". In some cases, this will be prefixed with "DOT", as in "DOT4209". The first two numbers in the code is the week of manufacture - 52 weeks in a year, remember. The last two are the year - in this case, the 09 represents 2009.
This can be approximated to the following - this is for the year 2010, and it will change slightly from year to year, but for the most part, this is how to convert the week number to the month:
01 - 05: January
06 - 09: February
10 - 14: March
15 - 18: April
19 - 22: May
23 - 27: June
28 - 31: July
32 - 35: August
36 - 40: September
41 - 44: October
45 - 48: November
49 - 52: December
Some tires will have a longer string of digits, like "NA2M4206" - in this case, it's the last four digits we are interested in, so this example would be the 42nd week of 2006.
What if your tire only has three digits? Throw it away! Tires made before 2000 used only one digit for the year. So a tire with the code "015" was made in January of 1995...or 1985!