There are 3 main types of microphone...

Dynamic

A dynamic microphone works very much the same was as a speaker but in the opposite direction. There's a cone that's attatched to a coil of wire. When the sound waves hit this cone, the coil of wire passes through the magnetic field of a magnet and the electronic signal is produced. They are mostly used for vocals as they don't work particurlarly well with high and low frequencies. They aren't very good at VERY LOUD and very quiet sounds as it takes quite a bit of energy to get the coil moving.
The microphone on the right is a Shure SM58, one of the most common dynamic mics, and the one with the most coppied shape.

Ribon

A Ribon microphone consists of a thin ribbon between two magnetic plates. When a sound wave interferes with the ribon, the electric current is interfered and this is then converted into the audio signal. They produce a very accurate representation of the original sound both with frequencies and clarity. But, ribbon microphones are not seen as being portable as they tend to be quite fragile. They are also quite expensive.

Condenser

A Condenser microphone basically uses a capacitor to pick the sound up. It has a thin diaphrap and a solid back place that picks up the sound. As the diaphram vibrates, the distance between the two plates changes and the value of the capacitance varies; thus creating the audio signal. These are usually used for picking up a quiet source at quite a distance. There are a few sub categories such as Dynamic condenser microphones, Cardioid condenser microphones and electret condenser microphones.

They also require an external (or sometimes internal - battery) source of power; typically 48v, also known as phantom power. (nb: sending phantom power to other microphones won't damage them.) This is usually supplied from the mixing desk. It can also be supplied by an inline box.