If you mean the rather old fashioned thermionic valves, Druiaghtagh, consisting of glowing hot stuff inside a glass bulb then their operation is surprisingly simple.
The essence is that the valve is sucked free of air, and a specially coated electrode, the cathode, is heated. Above this is another electrode at a high voltage positive with respect to the cathode, called the anode. When the cathode is heated and the high voltage applied, electrons flow through the vacuum from the cathode to the anode. Hey presto; a rectifier, a device allowing current in one direction only.
Next step, put a third electrode between the cathode and the anode with holes in it. With no potential on this third electrode, the control grid, the electrons flow unaffected through the holes. However, a very small potential on the grid causes a proportionately large variation in the electron flow. By varying the grid potential the cathode to anode current varies in proportion but to a greater extent. Hey double presto! An amplifier.
Finally, just to complicate things a bit further, more grids (screen and suppressor) are added to augment the attractiveness of the anode for the electrons in the former, and to stop the electrons bouncing off the anode and disrupting the electron flow in the latter.
Now comes the really clever stuff. Arrange for a high frequency signal to be added to the electron flow by forming an oscillator either by resonant feedback from anode to cathode and grid, or by injecting it from an external oscillator, then apply a low frequency signal, say an audio wave, to the grid. This will increase and decrease the amount of high frequency signal current present in the cathode/anode circuit in direct proportion to the grid signal voltage.
This is the basis of the simplest form of Amplitude Modulation. Even with the advent of robust solid state devices, some high power radio frequency transmission systems still use valves in the output sections.