How do I know whether to use the definite (the) or indefinite (a, an) article, and when to omit it altogether?
Use the definite article when you know which particular thing or set of things it is you're talking about.
We're going on a summer holiday! Let's get in the car.
The apples in my local shop look delicious.
Use the indefinite article when you don't know exactly which thing it is you're talking about.
I need a new car.
I'd love some apples.
Use no article when you're talking about the complete set of things.
I like cars.
Apples give me indigestion.
I've already come across one exception to this, so they are out there:
"That means the dog is a lot more efficient at making use of the nutrition in starch than the wolf." - BBC News
In this situation, they are referring to dog and wolf as particular species, rather than a particular dog or a particular wolf.
Definite vs Indefinite
(Bold is article used, Italics is word of interest)
To choose between these two kinds of articles:
You need to know if you are referring to any random object, or a specific one.
Let's say there are two people - John and Sam.
John: I need something to read.
Sam: Well, I can recommend a book.
John: That is my book!
Sam: John, I am not giving you the book back.
So, in the first example, John & Sam are talking about any book. So Sam uses 'a'. But in the second example, John is claiming a book to be his. Therefore, he & Sam are talking about a specific book: John's book.
Article vs No Article
Do not use any articles when you are not talking about an object by itself, but maybe a category or set of objects.
I like to read books.