There are two types of articles in English grammar, definite and indefinite, consisting of three words in total. These three words are "a," "an," and "the." The indefinite articles are "a" and "an." Remembering some simple rules can ensure choosing the proper article when speaking or writing in English.
The difference between definite articles and indefinite articles is that the definite article is used when referring to a specific person, place, idea, or thing, i.e. a noun, but the indefinite articles are used when referring to a noun in the more general sense. For example, if you were to say "Pass me the book," you would be referring to a specific book, and would therefore use the definite article. Conversely, if you said "Pass me a book," you are just referring to books in a general sense and could be referring to any book -- you are now using the indefinite article.
Remembering that indefinite articles refer to things in a more broad, general sense whereas definite articles reference specific things will help you to always use the correct phrase. Most native speakers of English use these words correctly without considering it, but it can become more confusing when learning English as a foreign language. Another thing to practice is remembering when to use "a" or when to use "an."
In general, the rule is to use "an" before words beginning with a vowel, and "a" before words beginning with a consonant. This means you would say "an apple," but "a car" or "a book." This rule often pertains more to the sound of the word, however, than the vowel/consonant at the beginning. For example, we say "a university," even though university begins with a vowel -- the word sounds like it begins with the consonant "y," however. Similarly, we would say "an umbrella," even though umbrella begins with a vowel.
There are certain times when an article is almost never used, and these include when referring to such things as geographic locations or names of countries. For example, you would not say "the Pennsylvania," or "the Lake Erie." When referring to a group of things, though, articles are generally used -- i.e., the United States. Articles are also not usually used when discussing general topics, such as "I like coffee," or "I enjoy kayaking."
It is not possible to list all of the instances where one might use definite or indefinite articles, or articles in general. Once you learn the general rules of articles in English, you must base most of your decisions when speaking or writing on what "sounds" best. There are many subtleties involved, and non-native speakers often tend to make mistakes with articles, even when they are otherwise fluent in English.