Dynamic microphone

The Shure SM58—the most popular dynamic mic in the world is as follows:

Dynamic microphones are the tough guys of microphones. They aren't usually delicate, due to the fact that they have very simple electronics. Dynamic microphones use a membrane to vibrate along with sound waves, moving a coil that is between two magnets. The vibration of the coil creates an electrical current that flows down a cable to be amplified. The amplifier used to boost the signal before sending that signal along to be used in recording is called a microphone pre-amp. The volume knob at the pre-amp is called a trim knob. This is what a dynamic mic looks like from inside:

The condenser microphone

The AKG Perception condenser microphone is shown as follows:

Condenser microphones are the sensitive type. The main difference between a condenser mic and a dynamic mic is that a condenser needs a little electricity to get the job done. It's less rugged than the dynamic mic and way more sensitive, so it usually lives in the studio instead of going out on stage.

Condenser microphones have a very thin, flat conductive sheet called a diaphram that is suspended in front of an electrified backplate. Any movement of the diaphragm disturbs the electrical field between them, making a signal. Condensers then take this information and have a bunch of circuitry that convert the signal into something our audio interface would like. It still needs a pre-amp. The signal is usually very detailed compared to the dynamic mic. If you plan on screaming a bunch, the dynamic may be a better choice. If you are a crooner, you should think about getting a condenser mic (although they tend to be more expensive). Here's what the inside of a condenser mic looks like:

If you are just starting to record things, I would suggest investing in a dynamic mic from a company like Shure, AKG, or Electro-Voice. They are well established and you can find them online for pretty reasonable prices.