The colon has primarily three grammatical uses and several non-grammatical uses.
Introducing a list
The colon is used to introduce a list of items.
The bookstore specializes in three subjects: art, architecture, and graphic design.
Do not, however, use a colon when the listed items are incorporated into the flow of the sentence.
Correct: The bookstore specializes in art, architecture, and graphic design.
Incorrect: The bookstore specializes in: art, architecture, and graphic design.
Between independent clauses when the second explains or illustrates the first
The colon is used to separate two independent clauses when the second explains or illustrates the first. In such usage, the colon functions in much the same way as the semicolon. As with the semicolon, do not capitalize the first word after the colon unless the word is ordinarily capitalized.
I have very little time to learn the language: my new job starts in five weeks.
A college degree is still worth something: a recent survey revealed that college graduates earned roughly 60% more than those with only a high school diploma.
All three of their children are involved in the arts: Richard is a sculptor, Diane is a pianist, and Julie is a theatre director.
When two or more sentences follow a colon, capitalize the first word following the colon.
He made three points: First, the company was losing over a million dollars each month. Second, the stock price was lower than it had ever been. Third, no banks were willing to loan the company any more money.
The colon can be used to emphasize a phrase or single word at the end of a sentence. An em dash can be used for the same purpose. In the second example below, an em dash is more common than a colon, though the use of a colon is nevertheless correct.
After three weeks of deliberation, the jury finally reached a verdict: guilty.
Five continents, three dozen countries, over a hundred cities: this was the trip of a lifetime.
Non-grammatical uses of the colon
The colon is used to separate hours from minutes, with no space before or after the colon.
The colon is used to express a ratio of two numbers, with no space before or after the colon.
The colon is used in biblical references to separate chapter from verse, with no space before or after the colon.
The colon is used to separate the volume from page numbers of a cited work, with no space before or after the colon.
Punctuation Quarterly 4:86–89 (read as “pages 86 through 89 of volume four”)
The colon is frequently used in business and personal correspondence.
Dear Ms. Smith:
cc: Tom Smith
Attention: Accounts Payable
PS: Don’t forget your swimsuit.