The rule I've always used is that if the first letter of the word immediately following it is a vowel, it's "an" and if it isn't use "a".

For example, "an apple" or "a potato". If there is an adjective, go by that first letter, for example "a large apple" or "an average potato".

Native English speaker here. This is incorrect, the "n" is added for phonetic help "a elephant" involves an awkward break between the two words, so enter "n" to help mouth muscles work around that.

This is the same reason for weird artifacts like: "a unicorn" because unicorn starts with. "Yoo" sound and so mouths don't need the help of the "n" to break up the awkwardness.