This is the most common use of indefinite articles. You should use "a" or "an" before any singular countable noun that is indefinite. For example, you say, “This morning I saw a dog.” Use "a" because the dog is not your dog nor the only dog in town; it is just one dog that you happened to see.
You say, “The show costs $20 a person,” or “I visit my relatives twice a year.” Using "a" or "an" in this way denotes frequency or allotment.
Using "a" or "an" in this way is a little old-fashioned, but you can still see and hear it used. "A" or "an" can be used in negative sentences to state emphatically “a single”. For example, you say, “We had not a thing to eat,” or “There was not a tree in sight.”
This is the most common use of "the." Use "the" when talking about definite things that your audience already knows about or that are obvious. For example, you say, “I spilled my drink on the carpet.” Use "the" because you did not spill your drink on just any carpet; it was a specific carpet in a specific place that your audience knows about.
Use "the" to refer to something that you have already mentioned. For example, you say, “I saw a dog this morning,” when you first mention the dog, but later you should say, “The dog looked hungry.” Every time you refer to the dog after this, you should use "the."
Use "the" to refer to things that are unique. For example, you say, “I saw the Queen of England.” There is only one Queen of England. If you say, “I saw a Queen of England,” you are implying that there are many queens of England.
Use "the" with superlatives. For example, you say, “This is the most expensive steak I have ever eaten,” or, “Russia is the biggest country in the world.” You use "the" for both of these examples because you are talking about single, unique and specific things.