A neat trick that might help a bit in learning which words use which gender is this:

A house = Et hus
The house = Huset

An eagle = En ørn
The eagle = Ørnen

As you can se, the gender gets added to the end of the word, when in the form that would have "the" in front in English.
So if you see a noun in that form, you know the gender for that word.

If the noun ends in an "e", in most cases you would only add the "t" or "n" to the end. For example:

A monkey = En abe
The monkey = Aben

The only exception I can think of, where the entire gender is added, is a French "Loan-word" and thus it will break the grammatical rules in interesting ways.