There are lots of different types of microphone but they all work in pretty similar ways.

Any noise travels through the air as a wave (imagine if you through a stone into a pond and watched the waves spreading out, well sound travels like that).

For a microphone to work it must somehow pick up these waves. So it needs something which vibrates when sound waves hit it. If you blow up a balloon and hold it next to your mouth when you speak you'll find it vibrates and this is similar to how this part of the microphone, called the diaphragm, works. Once you can detect the sound waves you then need to turn them into electric currents (so they can travel down wires, or be recorded onto tapes). Now this bit usually involves magnets.

As the diaphragm vibrates it moves a magnet (which it is connected to) back and forth. This magnet is surrounded by coils of wires and as the magnet moves it makes electric currents in the wires. These electric currents can then be turned back into sound by a speaker, which is simply a microphone, but in reverse.

In a speaker the magnet stays in the same place and there are coils of wire attached to another diaphragm. As the currents flow round the coil they create a magnetic force which makes the coil move (because of the big magnet around it) which in turn moves the diaphragm, which in turn makes the air vibrate which makes the sound.