You don't, you use the barrel code. If you don't have the original barrel you can try calling Remington.
Check the date code stamped on it. See related link
If this made sense I could answer better but if your asking for a date of a model 31 by serial you are better just looking at the date code stamp on the barrel. See related links for information on the Remington Society of America.
probably 200-400 depending on condition
anything that walks, flys or moves. 12 ga shotgun with shot or slugs give you the all around firearm.
About $150-$175, depending on condition.
50-250 or so
There's very few Remington things you can identify by just a serial but you got lucky ;) That is a Remington Model 1889 made in 1902. Value is greatly dependent on Condition, Condition, Condition, and Condition.
An H&R Sportsman with that serial number was made circa 1937-38. Value depends upon condition: Exellent $300 +/- $25, down to fair $125.
50-100 USD
Have it checked over by a gunsmith first.
Contact Remington
The serial number will not be any help in dating the gun,, it is dated on the barrel,,,,, check out this site to date the gun------http://www.remingtonsociety.com/rsa/questions/barrelcodes