How does frequency modulation work?

Frequency modulation (FM) works by taking a signal, such as an audio signal, and using it to modulate a higher frequency (Radio Frequency, RF) carrier. This modulation causes the RF to shift up and down in frequency. The RF remains relatively constant in amplitude, and its shifting frequency represents the original signal.

Contrast this with Amplitude Modulation (AM) where the RF is relatively constant in frequency, but its amplitude represents the original signal.

In order to recover the original signal in an FM system, the receiver must demodulate the signal by measuring the time between successive waves of the RF. In a typical broadcast band system, limitations in the the design requirements for tuning the modulated carrier and for demodulating the original signal force the tuning and demodulation to be done in different stages. Using a process known as superhetrodyning, the tuner amplifies the RF with a broad-band amplifier and mixes the RF with a local oscillator (LO) frequency, converting the RF into an intermediate frequency (IF), typically 10.7 MHz. It then passes the still modulated IF (or shifted RF) into a sharp band-pass filter, the IF stage, and removes the interference of other stations from the IF signal. It then demodulates the original signal from the IF signal.

Often, the original signal contains encoded information, such as a stereo subcarrier, which is subsequently demodulated and demultiplexed in order to recover the stereo signal. The question, however, asked about frequency modulation, so the answer stops here. If further detail is required, either add it by refining the answer, or comment on the question, and I or someone will refine the answer.