Vacuum tube DC amplifier circuit
First of all, vacuum tubes were not used as &quot;transistors&quot;.  They were, and still are, used as vacuum tubes.  Transistors and vacuum tubes are different things but either can be used as an amplifier.
Where transistors are primarily current amplifiers, vacuum tubes are voltage amplifiers.  The closest solid-state device to a vacuum tube (specifically a triode) is the JFET.
It is possible to get large amounts of amplification with vacuum tubes and examples are RF transmitters and RF amplifiers.  Even today there are some applications, such as very high powered radio transmitters that still use vacuum tubes.
To understand how you get this to happen, remember that P = VI.  To get more power you can increase either the current (I) or the voltage (V).  Transistors increase the current.  Vacuum tube amplifiers increase the voltage and can operate at very high voltages.  In some cases this is what you want but with others you want a relatively low voltage output.  For example audio amplification usually requires a low voltage low impedance (i.e. 8 Ohm) output.  To match the HV high-impedance output of a tube amplifier you will almost universally see output matching transformers on the output stages of a tube amplifier.  This steps-down the high voltage/low current signal to a low voltage/high current signal that you want for a speaker.