The similarity to the English word should help you with this one though! Hopefully.. :)
[ˈεˀg] = æg
Den Dansk Ordbog:
Wait, why can't you use "A" instead of "An"? I thought that was only in English...
Wow. I just realized that it comes before a word starting with a vowel. Wow.
It seems that the "g" in "æg" is always pronounced, but [ɛːˀɡ̊], [ɛjˀ], and [ɛwˀ] are listed as pronunciations.
Whenever a word takes 'et', attach it onto the end instead of en.
en pige = a girl
pigen = the girl
et æg = an egg
ægget = the egg
The egg technically isn't alive, it would be the embryo inside the egg that would be considered alive, but the advice "en is used for living things" is more a rule of thumb than a fixed rule. It's usually best to just learn the gender of the noun along with the noun.
There really aren't such rules in Danish nouns such as live or inaninate things, you gotta learn them from memory!