Electronic – How does a zener diode and a resistor regulate voltage

It's just the basic operating principle of a diode. An ideal diode would allow current to flow in one direction but block current flow in the other direction. This is based on how it's made, with a p-type region, an n-type region, and a depletion zone in between. Like the bottom diode in this picture:

When you apply a some voltage, in your case 0.9V then the p-type holes and the n-type electrons move into the depletion region because they are repelled by their respective battery terminal. With enough voltage (0.9V in your case) the free electrons in the depletion region get moving and current begins to flow like this:

Now in the ideal case if you were to reverse that battery the opposite will happen and you'll get no current flowing:

In the real world though you can only apply so much reverse voltage or push before you hit the breakdown voltage and current begins to flow freely in the reverse direction. Zener diodes take advantage of this fact and are constructed to breakdown at lower voltages such as your 3.3V.

Sources:
You can read more about how zeners are made here Or see the article I got all the pictures from here

Zener diode passes a lot of current (has low resistance) if the voltage is above Vz. So, connected in a circuit like in the question:

1. If the voltage at the output was lower than Vz, the diode would not conduct and (if there was o other load, the voltage would rise.
2. If the voltage at the output was higher than Vz, the diode would have low resistance and short out the output, which means that the voltage would drop (because of the resistor in series).

So, the circuit reaches an equilibrium of Vout=Vz. If the voltage tries to go lower (a load is connected), the diode conducts less and the voltage rises back up to Vz. If the voltage tries to go higher (aload was disconnected) then the diode would conduct more and drop the voltage down to Vz.