hi there
here is a basic block diagram of a transmitter and a receiver the transmitter at the top and the receiver below it....
The Oscillator in the transmitter could be a crystal or maybe a synthesiser
lets say it oscillates at 25MHz. So the transmitted signal is 25MHz. For a FM transmission commonly used for digital or voice, the modulation is applied to the oscillator as shown. In an AM transmitter, the modulation is usually applied to the final amplifier stage of the transmitter.
At the receiver, the received signal is very weak so first it is amplified and then it is mixed with the Local Oscillator (L.O.) signal. Again, like in the transmitter the L.O. could be a crystal or maybe a synthesiser. When you mix the incoming 25MHz with an appropriate L.O. signal you end up with a low frequency signal that you can Demodulate the audio from to send to a speaker.
The principals are the same if it was say a digital signal rather than an audio signal.
This is the basic system and there are many more complex variations. Some receivers may have 2 or 3 different Local Oscillators in them, quite common for very high frequency transmitters
cheers
Dave