I've seen many different types of microphones, and I feel like I should know some of most important ones before getting any farther. What are the most commonly mic types and how does one decide which to use?
There are a few major kinds of microphones:
Dynamic mics use an electromagnet attached to a diaphrahm. They're comparatively durable, so they generally can stand up to higher SPL. These are commonly used live, as well as for lound instruments like snare drums and guitar cabinets. A lot of really good ones are inexpensive as well (Shure SM57 and SM58, for example).
Condenser mics use a conductive diaphragm as part of a capacitor. Because of this, they require external power, referred to as phantom power. They are quite sensitive, particularly to high frequencies, but because of this they don't handle as much volume, so you don't usually see these as much up next to drums. But they're splendid for vocals and many instruments. Condensers come in large and small diaphragm variants.
Ribbon mics use a thin, very sensitive foil suspended in a magnetic field. They're extremely sensitive to transients and have a very wide frequency response, but they're expensive and delicate. In my opinion they sound simply amazing for vocals though.
These are the major types. There are exceptions to these of course - dynamics with a particularly wide and smooth frequency response, condensers that handle high SPL, and there's even at least one ribbon that takes phantom power, so while you should know these characteristics, in the end it is best to know the properties the mics you have access to.
Choosing a mic is a matter of fitting the right tool to the task at hand. Make sure you have a mic that can handle the appropriate SPL, that covers the frequencies you need covered, and most importantly, sounds good to you when you try it. Don't just choose one based on numbers, but try it out on whatever source you have. If you can, try a few mics that seem to fit the bill and choose the one you think sounds best.
And this might sound silly, but ask around! See what other people prefer for recording the kinds of things you are recording. Then give 'em a try :)
The most common types of microphones are condenser and dynamic.
In general, condenser microphones have a flat, extended frequency response, and are the best choice for far-proximity applications such as choirs and orchestras.
In general, dynamic microphones are good for near proximity, high SPL applications such as drums and individual instruments.
There are also certain microphones that are suitable for specific applications. The Shure SM-57 works particularly well for miking snare drums and electric guitar cabinets, for example, although it is also a great, rugged, inexpensive general purpose mic.
Shure and Audio Technica publish a wealth of excellent background and technical information about microphones and their proper use. If you read these publications and study microphone specification sheets, you will develop an excellent background of knowledge for effectively using the right type of microphones in almost any setting.
Audio Technica - A Brief Guide to Microphones