Check the markings on the barrel.
If it's stamped just as a Model 39 it was made between 1922 and 1938.
WARNING. If it is a Model 39 and the serial number doesn't start with "HS" the rifle is not safe to shoot with High Speed .22LR ammo.
These older models should be used ONLY with Standard Velocity ammo to prevent breaking the bolt.
These older models will have an octagon barrel and had color case hardened receivers.
The earlier Model 39 without a prefix to the serial number or with an "S" prefix are noted for the finer workmanship and quality.
After 1939 Marlin changed the model to the Model 39-A.
Marlin serial numbers are sometimes difficult to narrow down as to a manufacture date.
The very early Model 39 rifles and the original 97 models used straight serial numbers, but for some reason, all the online references I can find don't show any of the 1920's and 30's serial numbers.
If you look at straight serial numbers you'll get an 1897 model, and if you use a serial number prefix, you'll get post-war serial numbers.
Going on your serial number, if it's stamped just as a Model 39, it would probably have been made in 1922 or 1923.
Disassembly is pretty much like the newest versions.
Make sure it's empty.
Cock the hammer ALL THE WAY and open the lever just slightly. (If you don't cock the hammer all the way, when you disassemble the receiver the bolt and hammer will be damaged).
Unscrew the large thumb screw on the receiver. (Don't use a screwdriver it'll damage the slot, use a quarter. The screw is a captive screw and won't come all the way out. Just unscrew until it's completely loose in the receiver).
Holding the stock, gently bump the muzzle on a carpeted floor and the two receivers will separate.
Immediately lower the hammer to prevent accidentally pulling the trigger and allowing it to drop onto the receiver.
Push the bolt slightly to the rear and lift it out.
Notice that in the left receiver is a brass "box" with the ejector. In front of the ejector is what appears to be a silver screw with a notch in it.
This is actually a rivet.
Push the ejector down into the brass box with a screwdriver or punch and use a screwdriver to rotate the screw-like rivet about 1/3 of a turn. This locks the ejector down so you can get a cleaning rod into the barrel.
After cleaning, be sure to rotate the rivet to release the ejector.
To reassemble, put the bolt into the receiver and push it all the way forward.
Cock the hammer all the way.
Open the lever just slightly.
Insert the tongue on the right receiver into the half moon cut on the left receiver and push the two receivers together. DON'T FORCE ANYTHING.
If they don't want to seat, move the lever slightly back and forth and make sure the bolt is forward.
Tighten the thumb screw snuggly until the two receivers are fully seated and there is no "Step" between the two.
Make sure the action operates smoothly.
Here's a link to a current owner's manual:
http://stevespages.com/pdf/marlin_39a39m.pdf