How to tune an RF receiver with a microcontroller?
In simple terms by mixing (multiplying) a signal with a specific frequency (lets call it F) with a second frequency (lets call it G) you get two output frequencies F+G and F-G. If assuming that F is a high frequency then subtracting G gives you a lower frequency. Then by passing the signal through a band pass filter to eliminate unwanted frequencies you get a signal that something can be done with, demodulated and played over speakers, sampled and analyzed for digital content,... By using a micro to control the G frequency the micro can change the frequency from F that falls inside that band pass filter. 

Further if using a Superheteradine tuner the micro can control two different frequencies to give even greater frequency range.