Realistically, you can't.
Do an internet search.
Where did you find the serial number?
On a Colt revolver, the serial number is generally in two places. When you open the cylinder you will find the serial number at the base of the frame & crane.
From what I've learned on the Internet, the number on the butt is a government inventory control number. The serial number is stamped on the frame of the revolver; look for it after swinging out the cylinder.
Ruger has a serial number search function on the company web site.
The butt.
Look on the butt of the revolver
Call Colt
By it's model name & serial number.
By model and serial number. Go to proofhouse.com
By asking the factory to check their records on that serial number revolver. It may cost for the research.
On an older revolver, you are not likely to find a model number, since they did not use model numbers. If you remove the grips, you should find the serial number stamped in the frame under the grips.