You use "a" when referring to a noun without much precision, or when it's something rather general. "The" is used to refer to a specific object. Ex: There is a dog in the middle of the road. The dog is black. In the first sentence, you use "a" to refer to the dog because you haven't mentioned it before and you don't know any more details about it. In the second one, you would say "the dog" because you've already determined which dog it is; it's the one in the middle of the road.

Another good resource is http://owl.english.purdue.edu/owl/resource/540/01/ As mentioned a/an are 'indefinite articles' meaning they don't clearly specify a single thing. The is a 'definite article' meaning it points out a single specific example. Specific cases where you do not include an article are... Names of languages and nationalities: Chinese, English, Spanish, Russian (unless you are referring to the population of the nation: "The Spanish are known for their warm hospitality.") Names of sports: volleyball, hockey, baseball Names of academic subjects: mathematics, biology, history, computer science 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