The simplest “tester” is a filament/heater supply, an adjustable grid bias 0V to -18V (can be a 100K linear pot and 2 x PP3 batteries) and about 60V HT. A DMM is used to measure grid and anode voltage. A second cheap DMM is in series with the anode to HT. All other electrodes are either connected to 0V or HT. With this a simple check of filament/heater, emission and gm can be made. Of course with anything more complicated than a triode the gain and anode current is affected by g2 voltage. But at least you can tell if totally dead (no heater/filament or no emission) or alive.
Unless a tester can be used to quantify exact performance it’s of limited value today. This is because many tubes are not even available as NOS and most are no longer made, but a low emission tube may be a fail even though it works fine. In contrast some testers do not show up electrode leakage faults well which can be catastrophic.
Almost no tester measures RF performance as a Mixer, Oscillator or Amplifier. So being able to try the valve in a known good set (if heater/filament is OK and no shorts) is almost more useful than a Tube Tester. A Capacitor leakage tester that has 600V open circuit limited by 2 M ohms and a DMM can be used to verify there are no leaky electrodes (including Heater / Cathode) and the filament / heater continuity.
Types and details
Simple valve tester 1930s
Basic USA testers. Many are simple go/fail testers that really only test Triodes by measuring cathode current, on a Tetrode, Pentode or Hexode the Screen grid is tied to the anode.
Mullard High Speed Tester. Requires a card for the device under test and more for speed than exact performance.
AVO VCM163. More than a tester as it measures characteristics. You don’t need settings, can be set from the device data.
Ronald Dekker’s uTracer, a curve tracer. My own Blogging on it here.