I won't attempt to get into radio theory in this instructable, nor attempt to provide troubleshooting info on all that can go wrong. What I'll focus on, however, is what I've found to be wrong in the last five radios that I've resurrected, which is not vacuum tubes, but bad capacitors. Old electolytic, paper, and wax capacitors were never designed to last more than a couple of decades, therefore when you find a 50-70 year old radio that doesn't work properly, replacing the capacitors is a great place to start! Although a tube can certainly go bad, they can last almost indefinitely unless they are either subjected to rough handling, or subjected to excessive voltage from another component failure.
Also, if you attempt to work on one of these old radios, be very careful. It is not uncommon for some of these radios to use voltages in the hundreds of volts, and that can hurt, or worse! So, exercise caution. Don't work on it when it is plugged in, and be sure to discharge each capacitor (by shorting across the terminals) even when it is unplugged.
The radio I'll show in this instructable is a Zenith Wavemagnet radio that was manufactured sometime prior to March, 1942, making it almost 70 years old at the time of this Instructable. When I first powered up this radio, it would receive some stations, but had a loud hum, and the sound became very distorted after just a few minutes. The hum was a good indication that the filter cap's were bad, and the distortion turned out to be due to one bad paper capacitor.