A / An / The

What is an article? Basically, an article is an adjective. Like adjectives, articles modify nouns. English has two articles: the and a/an. "The" is used to refer to specific or particular nouns; "a/an" is used to modify non-specific or non-particular nouns. We call the the definite article and a/an the indefinite article.
the = definite article
a/an = indefinite article
For example, if I say, "Let's read the book," I mean a specific book. If I say, "Let's read a book," I mean any book rather than a specific book. Here's another way to explain it: The is used to refer to a specific or particular member of a group. For example, "I just saw the most popular movie of the year." There are many movies, but only one particular movie is the most popular. Therefore, we use the. "A/an" is used to refer to a non-specific or non-particular member of the group. For example, "I would like to go see a movie." Here, we're not talking about a specific movie. We're talking about any movie. There are many movies, and I want to see any movie. I don't have a specific one in mind. Let's look at each kind of article a little more closely.
Indefinite Articles: a and an
"A" and "an" signal that the noun modified is indefinite, referring to any member of a group. For example:

* "My daughter really wants a dog for Christmas." This refers to any dog. We don't know which dog because we haven't found the dog yet.
* "Somebody call a policeman!" This refers to any policeman. We don't need a specific policeman; we need any policeman who is available.
* "When I was at the zoo, I saw an elephant!" Here, we're talking about a single, non-specific thing, in this case an elephant. There are probably several elephants at the zoo, but there's only one we're talking about here.

Remember, using a or an depends on the sound that begins the next word. So...

* a + singular noun beginning with a consonant: a boy; a car; a bike; a zoo; a dog
* an + singular noun beginning with a vowel: an elephant; an egg; an apple; an idiot; an orphan
* a + singular noun beginning with a consonant sound: a user (sounds like 'yoo-zer,' i.e. begins with a consonant 'y' sound, so 'a' is used); a university; a unicycle
* In some cases where "h" is pronounced, such as "historical," us an:

An historical event is worth recording.
In writing, "a historical event" is more commonly used.
Remember that this rule also applies when you use acronyms:
Introductory Composition at Purdue (ICaP) handles first-year writing at the University. Therefore, an ICaP memo generally discusses issues concerning English 106 instructors. Another case where this rule applies is when acronyms start with consonant letters but have vowel sounds:
An MSDS (material safety data sheet) was used to record the data. An SPCC plan (Spill Prevention Control and Countermeasures plan) will help us prepare for the worst. If the noun is modified by an adjective, the choice between a and an depends on the initial sound of the adjective that immediately follows the article:

* a broken egg
* an unusual problem
* a European country (sounds like 'yer-o-pi-an,' i.e. begins with consonant 'y' sound)

Remember, too, that in English, the indefinite articles are used to indicate membership in a group:

* I am a teacher. (I am a member of a large group known as teachers.)
* Brian is an Irishman. (Brian is a member of the people known as Irish.)
* Seiko is a practicing Buddhist. (Seiko is a member of the group of people known as Buddhists.)

Definite Article: the
The definite article is used before singular and plural nouns when the noun is specific or particular. The signals that the noun is definite, that it refers to a particular member of a group. For example:
"The dog that bit me ran away." Here, we're talking about a specific dog, the dog that bit me.
"I was happy to see the policeman who saved my cat!" Here, we're talking about a particular policeman. Even if we don't know the policeman's name, it's still a particular policeman because it is the one who saved the cat.
"I saw the elephant at the zoo." Here, we're talking about a specific noun. Probably there is only one elephant at the zoo.
Count and Noncount Nouns
The can be used with noncount nouns, or the article can be omitted entirely.

* "I love to sail over the water" (some specific body of water) or "I love to sail over water" (any water).
* "He spilled the milk all over the floor" (some specific milk, perhaps the milk you bought earlier that day) or "He spilled milk all over the floor" (any milk).

"A/an" can be used only with count nouns.

* "I need a bottle of water."
* "I need a new glass of milk."

Most of the time, you can't say, "She wants a water," unless you're implying, say, a bottle of water.
Geographical use of the
There are some specific rules for using the with geographical nouns. Do not use the before:

* names of most countries/territories: Italy, Mexico, Bolivia; however, the Netherlands, the Dominican Republic, the Philippines, the United States
* names of cities, towns, or states: Seoul, Manitoba, Miami
* names of streets: Washington Blvd., Main St.
* names of lakes and bays: Lake Titicaca, Lake Erie except with a group of lakes like the Great Lakes
* names of mountains: Mount Everest, Mount Fuji except with ranges of mountains like the Andes or the Rockies or unusual names like the Matterhorn
* names of continents (Asia, Europe)
* names of islands (Easter Island, Maui, Key West) except with island chains like the Aleutians, the Hebrides, or the Canary Islands

Do use the before:

* names of rivers, oceans and seas: the Nile, the Pacific
* points on the globe: the Equator, the North Pole
* geographical areas: the Middle East, the West
* deserts, forests, gulfs, and peninsulas: the Sahara, the Persian Gulf, the Black Forest, the Iberian Peninsula

Omission of Articles
Some common types of nouns that don't take an article are:

* Names of languages and nationalities: Chinese, English, Spanish, Russian
* Names of sports: volleyball, hockey, baseball
* Names of academic subjects: mathematics, biology, history, computer science