The Simple Rules
The articles a and an mean exactly the same thing. They are indefinite articles and are used before countable non-specific nouns (e.g., balloon, table, egg). The only different between them is their sound. You choose one or the other based only on the sound of the letter that comes next.
Simply put, if the sound is a vowel (a,e,i,o,u) you use an, and if the sound is a consonant (all other letters in the alphabet) you use a.
an alien a balloon an end a couch an island a drum an oyster a flower an umbrella
However, there are some tricky exceptions. Like I mentioned, the choice should be made based on the sound and sometimes a vowel sounds like a consonant and sometimes a consonant sounds like a vowel. For example, many abbreviations that start with the letter M use an because the letter M is pronounced “em.” For example, “Billy has an M.A. in Customer Relations.”
Likewise, a vowel might sound like a consonant. This is especially true for the letter U, and the combination EU. Words that start with a “yu” sound (urinal, useful, eulogy, eukaryote) should be preceded by a.
Other words starting with U have the “uh” sound (umbrella, uplift, under) – these use a because “uh” is a vowel sound.
After a while, choosing the correct article becomes very easy because it feels comfortable to say it. Try saying “a alien.” You’ll notice that there’s an uncomfortable stop between words – like you’re blowing air out of your throat twice. But, when you say it correctly, “an alien,” the two words almost become one word with a very smooth and easy transition.
In the same way, if you try to put an in front of a word that starts with a consonant, you’ll have trouble jumping from one word to another: “an toy.” The an sounds too forced. The two words don’t mix with each other very well.