How can I find out the year a colt 38 revolver was made with serial number 157381?

Colt Firearm Serial Number Lookup Year of Manufacture

If you can not locate your serial # on this site, there is a toll free number to call for assistance as well.

Looks like a 1931, But you decide..

1950
OFFICERS MODEL SPECIAL 1931
POLICE POSITIVE .38 1931
BANKERS SPECIAL 1929
SINGLE ACTION ARMY & BISLEY REVOLVERS 1928
POLICE POSITIVE SPECIAL & DETECTIVE SPECIAL 1926
1908 HAMMERLESS .25 1920
1903 HAMMERLESS .32 1918
MODEL 1911 MILITARY 1913
ARMY SPECIAL & OFFICERS MODEL

Call colt. 1-800-962-COLT (2658)

The Colt "DA" (Dept. of the Army) was manufactured Between 1892 and 1942 and are considered to be Pre War (WWII) the SN Look-up on Colt's site does not give a specific year (http://www.colt.com/CustomerServices/SerialNumberLookup.aspx) but they do have an archive service that (for a fee) will research the gun for you and give you details on it origin.

Here ya go, a list of Colt information by Serial Number/Date Made.
http://www.sightm1911.com/1911Production.htm

The weapon's condition is really needed to be known before being able to provide information like this. And to know its condition, it really needs to be inspected thoroughly. Take it to a valuer or firearms enthusiast to try and gauge a proper amount.

Colt