"A" vs. "The"

Many English students have trouble with when to use "a", and when to use "the". It seems like a small thing to worry about, but there is a very big difference and misuse can result in confusion in conversations.

"A" is used to introduce a noun into a conversation for the first time. "A" indicates a single noun, whereas if the noun is plural, "a" is not used. For example:
I bought a new camera.
I bought two new cameras.
"A" also becomes "An" when places before words that begin with a vowel sounds (a,e,i,o,u).
I bought an orange at the supermarket.
I spent an hour watching television.
"The" is used in place of "a":
After the noun has been introduced to the listener and is being referred to a second time. Example: I took a camera with me to the top of the mountain, but the camera didn't have batteries.
With nouns of which there is only one. Example: I want to clean up the environment on the moon.
With nouns which represent a larger institution or concept for a place. Examples: the post office, the hospital, the army, the park, the beach
With many location names and in the names of countries which have a plural feeling. Examples: The United States, The Phillipines, The Mediterranean Sea, The Cayman Islands
Here are some more examples which show the proper uses of "a" and "the":

I ate at a restaurant in Shibuya. (First time being introduced, and the listener does not know which restaurant precisely)
I at at the restaurant in Shibuya near your house. (First time introduced, but the listener likely knows exactly which restaurant this is.)

I want a new phone. (Non-specific about what type of phone; listener does not know which model. Perhaps the speaker has not decided which model yet.)
I want the new model of phone from Sony. (Specific, and the listener likely knows which model is being talked about.)

Using "a" and "the" correctly is an important step to becoming an effective English communicator. Do your best, and remember that it is an important difference!