If an FM signal has different frequencies, how does the radio receive the signal in a fixed frequency?
The frequency you tune to is the centre frequency of the spectrum created by the modulation. The input from the aerial is generally modulated down to an intermediate frequency (to make it easier to work with) and then fed into a Phase-Locked Loop (PLL) circuit which creates a signal proportional to the frequency shift from the centre frequency. This signal turns out to be the originally encoded audio (if you work through the maths).

As an aside note, the centre frequencies of stations (103.2MHz, 102.4MHZ etc) will be deliberately spaced out in order to avoid overlap between one station and another. This is controlled by the local spectrum licensing agency in your region. Without this, when you tuned to one station you would get interference from other stations broadcasting at a similar frequency.

This site has a decent simple explanation of the basic principles and this is an excellent old US Army video on the subject.