When should "an" be used before a word and when should "a" be used before a word? I thought that "an" was used before a word beginning with a vowel...

You honestly have to listen to what you are saying/writing. It is mostly executed based on phonetic sound. MTV has the first letter as "M". It SOUNDS like "emcee, eminem, enema". When it comes to letters, you go with how you think you would spell it: M = EM (at least that is how I would spell it if I had to). Since I would spell the letter beginning with an "E", I would use an "an". The sound will tip you off every time. If it is a little awkward to say, then it is probably wrong. You wouldn't say "a hour, an opossum (my fave), an hug". But there are some definitive rules that can help that I teach my students:

"A" goes before consonants such as "cat, dog, fish".

-But- you put an "An" before an "h" that does not carry a sound(meaning you hear the sound of the vowel behind it) such as "hour, honor" not "high, home"

"An" goes before vowel such as "orange, apple, emu"

-But- you put an "A" in front of words that start with "u" but have a "y" sound like in the word "you" or an "o" that have a "w" sound like in the word "won" such as "union, usurper, unicorn" and "one"