How wireless works

Wireless works because an electromagnetic wave, passing through the air at the speed of light, can create - or 'induce' - an electrical signal in an aerial. If you can control this electromagnetic wave, then you can use it to communicate or to broadcast information.So in a radio system, information is sent from one place - the transmitter - and picked up in another - the receiver - using an electromagnetic wave to carry it.

Magnetism through the air : sending all the right signals
Transmitters and receivers sit at each end of a wireless system, using an aerial or antenna at each end. At the transmitter, the electrical signals leave the antenna to create electromagnetic waves that radiate outwards. Broadcast station antennas spread their power evenly and send out waves in all directions, whereas the power in a communications antenna (generally a satellite dish for example) tends to be focussed and pointed in a single direction.
At the receiver, the electromagnetic waves create or 'induce' small electrical signals in the antenna, which are picked up by an electrical circuit. The signal is usually very small, and needs to be amplified before it can be processed.
Longer wavelengths are picked up better by longer aerials, but short wavelengths - like the microwaves used in mobile phone systems - can be picked up by shorter aerials.

Modulation : carrying the message
When Marconi first transmitted across the Atlantic, it was enough simply to detect the presence (or absence!) of the radio wave. The long and short pulses of Morse code supplied the information. Today, the information is piggy-backed onto a 'carrier' wave. This is called 'modulation'. When it's received, the carrier wave is stripped off and ignored, leaving only the 'demodulated' information behind.
When you tune your radio to a particular station, you are actually selecting the frequency of its carrier wave.
The MW and LW bands on your radio use amplitude modulation or AM. The information is 'added' to the carrier wave, producing a signal that's stronger on loud notes and weaker on quiet ones. The carrier wave is 'subtracted' by your transistor so you just get the music.
FM stands for 'frequency modulation'. The information signal modifies the carrier wave by changing its frequency very slightly. Because the strength of the carrier wave never varies, FM radio is much less noisy than AM radio and gives far better quality as a result.