An empty space won't pass any current (at reasonable voltages).
If you put a very hot metal electrode in an empty space, electrons boil off. We call it "cathode".
If you put in a second electrode, the "anode" or "plate" that is more positive than the first, the electrons will flow to the plate.
The number of electrons is a function of the size of the cathode, the cathode-plate distance, and the voltage on the plate. In normal operation, the first two values are fixed in the factory, but you can change the voltage and that changes the current.
If you put a resistor between the plate and the battery, the current causes a voltage drop in the resistor. If you change the battery voltage, the current changes, and the voltage drop changes.
If the plate is negative of the cathode, no electrons flow. Already we have a rectifier.
You have a positive plate flowing current. Put a wire-mesh fence or "grid" between the cathode and plate. If you put a voltage from grid to cathode, the electrons coming off the cathode feel the voltages on both the plate and the grid. The grid is closer and has more effect. If the grid is negative, no electrons flow to it. Now a small change in grid voltage, without any grid current, can cause a large change in plate current. If you have a plate resistor, now you can change its voltage drop a lot with a small change of grid voltage.
If the grid goes positive of the cathode, it sucks many of the electrons that would otherwise flow to the plate. Now it is hard work to change the grid voltage. In most audio systems we do not let the grid go positive of the cathode.
> a MOSFET transistor is most similar to a tube
A vacuum tube is an FET. FETs differ in what they use for a channel (empty space or a crystal) and how they insulate the control electrode. Vacuum tubes and JFETs use a diode as the control electrode: when negative, no current flows, and positive-grid/gate operation is unusual. MOSFETs have a glass insulator and the gate can be driven with any voltage (up to ~100V for thin glass, but there is usually a 20V protection diode, and normally there is no point in driving the grid higher than 4 or 5 volts).
While these are all FETs, they are made in different shapes. A vacuum tube normally has its control grid blocking the electron path. JFETs and MOSFETs put the control gate on the side of the current path and pinch-off the current flow. Wide variations of length and thickness can give a variety of response curves.
I've always considered JFETs to be tube-like, because they will suck grid current, so are normally operated negative-gate, and because MOSFETs have been much noisier than vacuum triodes or JFETs. But yeah, as a first approximation a MOSFET is a tube that works best with a positive gate not drawing current.
> I am confused on how gain is established.
In triodes, both the grid and plate affect plate current. The grid has the most effect, but a large swing of plate voltage will negate the change of grid voltage. That means there is a maximum possible voltage amplification, the Amplification Factor or Mu. In real life, you never get that much gain, 70% to 50% of Mu is doing good.
It is possible to plot the voltage gain from the plate curve diagram. But that is hard work, the diagrams are imprecise, and typical voltage amplifiers work at the very bottom of a plate curve diagram drawn to show the whole useful range of the tube.
What you really do is turn to the back of the tube manual, to the Resistance Coupled Amplifier chart. This lists the tubes commonly used for voltage amplifiers, suggested values, and performance data. Find a condition similar to yours and steal it. Remember that 99% of The Old Men were no smarter than you, and the 1% did the calculations and tables that made tube-design easy for all the others.
