If an FM signal has different frequencies according to the modulation, how does the radio receive the signal in a fixed frequency like 103.2 MHz?
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.
For FM, Carson's bandwidth rule informs you the approximate bandwidth of a transmission. The bandwidth value it calculates contains 98% of the energy of the whole transmission. It is expressed by the relation CBR = 2 (\$\Delta\$ f + f\$_M\$) where CBR is the bandwidth requirement, \$\Delta\$ f is the peak frequency deviation, and f\$_M\$ is the highest frequency in the modulating signal.
This means that a totally unmodulated waveform has zero bandwidth but this is clearly not the case when modulation occurs. The radio receiver has a bandwidth that is wide enough to accommodate the modulation but small enough to reject unwanted transmissions in adjacent channels.
Here's what AM and FM look like: -
It should be clear that the carrier in the FM system contains a range of frequencies for the simple modulation by a pure sine wave. It gets complicated when composite signals modulate the carrier of course but the principle is the same.
Pretty picture stolen from here
The answers above are correct but have missed out on one important part of the FM channel. They all have a 19kHz pilot signal to let the reciever know that there is a stereo signal to be decoded.
Any signal in the FM band without this pilot tone are ignored. See here for more info.