The date code should be part of the DOT number. It will usually be on 1 side, near the bead of the tire.
I think they add a number per decade. But the last 3 numbers will generally be the week/and year. IE: DOT gkur-2345-523*, the 523 would mean the tire was made the 52nd week of 2003 or 2013, depending on the total number of digits in the whole DOT number.
*completely made up number.
And as an FYI the other numbers should tell you where the tire was made (that gkur, I put on my made up number, should be similar to a Goodyear) and the other numbers will likely be the manufacturers numbers.
When a tire is retreaded, the retreaders add and additional DOT stamp near the original, that gives the same info.