Saylor.org's English Composition/Articles

The articles in English are the definite article 'the' and the indefinite articles 'a' and 'an' (and sometimes some).

The rules of English grammar require that in most cases a noun, or more generally a noun phrase, must be "completed" with a determiner to clarify what is the referent of the noun phrase.[1] The most common determiners are the articles the and a(n), which specify the presence or absence of definiteness of the noun. Other possible determiners include words like this, my, each and many – see English determiners. There are also cases where no determiner is required, as in the sentence John likes fast cars.

The definite article the is used when the referent of the noun phrase is assumed to be unique or known from the context. For example, in the sentence The boy with glasses was looking at the moon, it is assumed that in the context there will be only one boy with glasses, and only one moon, that could be being referred to. However the definite article is not used:

with generic nouns (plural or uncountable): cars have accelerators, happiness is contagious, referring to cars in general and happiness in general (compare the happiness I felt yesterday, specifying particular happiness);
with many proper names: John, France, London, etc.

The indefinite article a (before a consonant sound) or an (before a vowel sound) is used only with singular, countable nouns. It indicates that the referent of the noun phrase is one unspecified member of a class. For example, in the sentence An ugly man was smoking a pipe, it is assumed that in the context there is no specific ugly man, and no specific pipe, that is known to be being referred to.

With plural or uncountable nouns when the referent is indefinite, zero article is often used (the same as in the generic definite case described above). However in such situations the determiner some is often added (or rather any in negative contexts and many questions). For example:

There are apples in the kitchen or There are some apples in the kitchen;
We do not have information or We do not have any information;
Would you like tea? or Would you like some tea? or Would you like any tea?

Additionally, articles are not normally used:

in noun phrases that contain other determiners (my house, this cat, America's history), although it is possible to combine articles with certain other determiners, as in the many issues, such a child
with pronouns (he, nobody), although again certain combinations are possible (as the one, the many, the few).
preceding noun phrases consisting of a clause or infinitive phrase (what you've done is very good, to surrender is to die).