How does a microwave oven modulate its output power?
It's really simple.  They have one fixed power level, and turn it on and off.  You can hear it when it is on low power.  It'll hum louder for a few seconds, then have a longer period when it is a little quieter.  On is louder, off is quieter.

On full power, it is on all the time.  Lower power switches it off for a short pause with a longer on period.  Low power is a short on period followed by a longer off period.

It is sort of pulse width modulation, but real slow.



The frequency of the microwaves is fixed.  More or less - it isn't strictly controlled because it isn't critical.  The construction of the magnetron sets the frequency - you can't easily vary it.  The frequency is more of a range of frequencies.

Modulating the power of a 1000 watt transmitter isn't easy, so the manufacturers don't try.  A fixed power level is enough, if you can turn it on and off.  

They don't even closely regulate the power all that closely.  The transformer is made such that it limits the current to the magnetron, and that's about all the regulation there is.