Articles: a, an, the

a vs. an

Use a before a singular noun beginning with a consonant sound. Use an before a singular noun beginning with a vowel sound.
 
consonant  consonant sound vowel vowel sound
a box a European an orange an honor
a hand a one-armed man an apple an hour
a clock a university an effort
a word a unique idea an umbrella
a lamp an introduction
 

a, an vs. the

A/an  are indefinite articles. 
The is a definite article.
Think of the as a replacement for a/an when the object is known.
 

Albert sat down in a chair. He didn't realize that the chair was broken.

When I  say a, I expect that you don't know what I'm talking about.
When I say the, I know that you know what I am talking about.
 

The sun rises at 5:24 a.m. and sets at 8:29 p.m.. 
Would you please shut the window? It's cold in here.
 

a, an vs. no article
Use a only with singular countable nouns.
Use no article with uncountable nouns
 

The woman's hair was brown. She found a long hair on his shirt.
Life is wonderful. Franklin had an interesting life.
I like coffee better than tea. Would you like a cup of tea?
Nam knows lots of new vocabulary. I taught him 10 new words.
 
Use a with a singular countable noun, but no article with plural nouns.
 
India is a warm country. India and Mexico are warm countries.
Puna is an intelligent student. Puna and Maria are intelligent students.

Use the before superlative expressions.
 

Pluto is the farthest planet from the Sun.
Mario thinks Italy has the best football team.
The most expensive restaurant in town is Le Cirque.

With expressions such as kind of and type of, use the with a statement, but don't use a or an in a question.
 

What kind of computer  do you have. He's the type of student that succeeds.
What brand of car do you like? That's the sort of thing I had in mind.
 
 Use no article with gerunds.
 
Running is good exercise.
Reading is the best thing to do to improve your writing.

Don't use the with place names. Use the with names which contain the category.
 

Hong Kong the Hudson River
Europe the Balkan peninsula*
Afganistan the Panama Canal
Illinois the Indian Ocean

Here are some exceptions to this rule:
 

Victoria Falls Jones Beach
Central Park Oxford University

Some plurals require the:
 

the Philippines the Great Lakes
the Andes the Antilles

Don't use the with street names:
 
 

Macy's Department store is on 34th Street between Broadway and Seventh Avenue in New York City.

Note: There are many other rules and conventions for using the, a, and an. It takes most second-language learners a long time to use them well. The best we to learn them is to be aware of their use in your reading and as you hear native-speakers of English talk. Be careful, it is easy to miss a and the when native speakers talk. They are small sounds and you will not always hear them.
 

* Peninsula: an area of land almost surrounded by water or projecting far into the sea.

Practice #1
Practice #2
Practice #3

(c) David Tillyer, 1998