Go to: http://www.remington.com/products/archived/centerfire/autoloading/model-742-woodsmaster.aspx
look up the serial block number on the firearm compared to what the dates are on the link. Its not exact but it gives you a approximate time
1920
Need to check the barrel date code. Remington Society of America, Manufacture date link has all the details.
Remington Works - 1914 (late)
It's date stamped, check the manufacture date page on the Remington Society of America for details.
1912
1920
1924
1923
1912
1912
1919
1913