English nouns are plain words -- remember those Schoolhouse Rock shorts? A "person, place, or thing". The noun "man" for example, refers to a human of the male gender. If we want to reference a specific man, we have to say "the man", meaning "that specific one there". To reference any man, we have to add the particle "a" and say "a man", meaning "any man".

Irish has no article 'a' or 'an', it's considered to be included in the word itself. So when we use the noun man -- fear -- it means "a man" automatically. We don't have to add any extra bits to it.

However, there is an article 'the', which takes several forms, depending on whether the nouns are singular or plural.

with a singular noun	an
with a plural noun	na

If the noun following the plural article na begins with a vowel, add an h-. This is not the same as lenition, it is added before the vowel instead of after the first letter.

In addition, the article 'an' affects the nouns that follow it in a number of ways.

first letter of noun	masculine nouns	feminine nouns
consonant	no change	lenition (not d, l, n, r, s, or t)
letter s	no change	change to ts (not sc, sl, sm, sp, or st)
vowel	add 't-'	no change

It is often easy to determine if a noun in Irish is masculine or feminine simply by how it appears with 'an'. If it is lenited (the second letter is h), it begins with ts, or an unchanged vowel, it is feminine. If it is not lenited, or begins with 't-' then it is masculine. It's a good guess, at least.