Instructions
Turn off the radio and make certain it is unplugged. If you were using it, give it a few minutes to allow the tubes to cool.
Remove the back of the radio. They're attached all kinds of ways. Some used hexagonal screws, some Phillips head or flat head screws; some are little more than thick cardboard held in place with clips, and some are plastic, wood or cardboard that slips into a groove. However it is attached, remove the back to expose the radios inner workings.
Check the inside back portion of the cover. Occasionally those crafty old radio makers put the model numbers on the inside to prevent the wear and tear and overall deterioration that can occur on the outside. If there are no identifying marks on the inside or inside cover, you will still be able to determine the vintage and model using identification of the tubes and a little research.
Find the most accessible bulb, grasp it lightly but firmly, and give it a wiggle. Remember to handle the bulb with care. The bulbs are fragile to begin with and become more brittle with age. Gently remove the bulb from its socket.
Examine the non-glass base of the bulb, and look for identifying marks on the bulb. If you find numbers like 01, 01A, WD-11,WD-12 112 and 120, the bulbs were built in the early 1920s through 1926, and it's likely the age of your radio is somewhere in that range.
Count the number of pins on the bottom of the bulb. Tubes with four pins are generally from the early and mid 1920s. Radios with four to seven larger, thicker pins are likely from the late 1920s through the 1930s. Radios with eight pins, referred to as octal tubes, are primarily are from the mid 1930s through the 1950s. Radios with eight thin wire-like pins (loctal tubes) are likely from the late 1930s through 1950s. Tubes that have either seven or nine wire-like pins were commonly used from the mid 1940s through the 1960s. This is only a rough guide; there are exceptions to every rule.
Look at the tube itself. Some tubes were built with certain peculiarities that may further narrow the year in which the tube was commonly used. A tube with four to seven pins and a small metal nipple, called a grid cap, on top was made around 1929. If the tube is all metal with no glass, it was made in 1935 or later.
Using the references, there are numerous resources that will include pictures of the various antique radios. Since you've narrowed the age range by the bulb, follow the model and there is a good chance you will find your radio among the hundreds, perhaps thousands, of photos contained in the reference material. Failing that, the "Bible" of antique radios is a book entitled "The Collector's Guide to Antique Radios" by John Slusser. The book is praised universally by vintage radio collectors. Seek it out at your local library op local electronics store, or order it online.
Contact the manufacturer. The maker may be able to identify for you the model you own given the information you've collected on the tubes and approximate age, perhaps right down to its location of manufacture. If all else fails, seek local antique radio collectors online. You'll be amazed how many people collect and congregate in forums all over the Internet.