The is the definite article. It is used before singular or plural nouns that are specific or particular. Here are some examples:
"The girl who lives next door to me is really cute." This refers to a particular girl: the girl who lives next door.
"The president is a busy man." There is only one president, so we are referring to a specific noun here.
"I love the books you gave me." Again, we're talking about particular books, the ones you gave me.
A/an are the indefinite articles. We use a/an before general, non-specific nouns or to indicate membership in a group. A/an can only be used with countable, singular nouns. Here are some examples of how to use a/an:
"Let's go see a movie tonight." Here we aren't talking about a specific movie, as we haven't said which movie we want to see.
"Cassie is an interpreter." Here, Cassie belongs to a group: interpreters. We use "an" instead of "a" because "interpreter" begins with a vowell.
"I hope I get a car for my birthday." This refers to any car. We don't know which car yet because we haven't gotten the car.
Finally, all articles in English are invariable, meaning that they do not change if the noun is singular or plural, male or female. There are no other forms of the, an, or a.