Am radio transmitters use an occillator to generate a high frequency tone - this is the broadcast frequency - which varies in amplitude according to the sounds fed into it. The receiver uses a simple circuit to extract the audio information.
FM is a bit more complex, based on varying the frequency.
These pages give a simple guide:
http://entertainment.howstuffworks.com/radio.htm
And in addition.
The modern modulation methods use a system called "opti mod" that adjusts the transmitter modulation power as the sound level in the broadcast studio varies. thus obtaining a relatively stable volume level on your radio receiver.