Here's a circuit for a series string amp and in all respects it is typical of the breed although you sometimes see these with four, fiver, and sometimes more tubes. The idea's the same.
In a never ending quest for ever less expensive radios, RCA released model schematics for what are known as All American Five radios.
By putting the filaments in series and adding a suitable resistance, a power supply of a sort could be cobbled up without buying a power transformer. The typical offering in a guitar amp works on the same principle. Get as close as you can to 120v with the filaments in series, add in enough resistance to make up the difference, a couple of good stout electrolytic capacitors and use the chassis as the return path and Bob's yer uncle as the Brits say.
Well. In a radio it's usually sitting on a shelf inside a plastic or wood cabinet and you only touch a plastic knob so what's the worry? The Arvin folks, known then, as now for their metal stamping expertise released a line of metal case radios using this technology but did a baked enamel finish that is a pretty good insulator. Sometimes I cringe when I see people who have stripped and chrome plated these sets but nevermind. The subject's guitar amps.
The evil here consists of two things-the chassis as a return path for line voltage, and the guitarist or harp player's intimate connection to that return path through the guitar or mic cable. Standing barefoot on a cement floor or wearing sweaty leather shoes only makes it more dangerous. You can get the whole 120v of AC through your hands or mouth and it CAN kill you.
There is one, and only one, way of making this safe to use and that is through the use of an isolation transformer. That is a device which ISOLATES the circuit thus described from line voltage and thus saves you from being the ground return path. There is NO other way. A three prong cord will not make you safe.
You can obtain isolation transformers pretty easily from a number of sources or, you can make your own using a pair of Radio Shack door bell transformers back-to-back and accomplish the same goal.
Having said all that, these can be really fun amps to play with, but be advised: They're not really safe in their unmodified state.
UPDATE: One of my colleagues has posed the question of using a GFCI self contained cord with these amps. I myself have not used them, and the idea seems to be OK, but I think the difference is that with a GFCI setup you're interrupting a potentially dangerous problem, and depending on a relay to do it. I think the difference is that relays do not always do what you want when you want, and the problem is always there-a hot chassis connected to one side of the line. With a suitable isolation transformer, you eliminate the hot chassis problem completely and totally forever.