The colon is a versatile punctuation mark. Here are its three primary functions, followed by a few other uses:
Definition or Expansion
“But here’s the interesting thing: He hadn’t ever been there before.”
Note the capitalization of the first word after the colon. All usage
guides agree that in a sentence like “I want you to tell me one thing:
the truth,” the first word should be lowercase because it begins a
phrase, not a complete sentence. But handbooks are divided over whether
to capitalize complete sentences.
The Chicago Manual of Style advises doing so only when the
defining or expanding passage following the colon consists of two or
more sentences. Others disagree, and though I usually follow Chicago,
I concur with them: It can be difficult in a passage to know when the
definition or expansion ends, and the distinction between a single
sentence and two or more seems trivial and inconsistent.
Setting up a Quotation
He makes this moral argument: “Taking whatever we need from the world
to support our comfortable lives is not worthy of us as moral beings.”
Note that the colon concludes an independent clause that introduces a
statement; it brings the reader to a temporary halt. Writers, ignoring
the grammatical distinction between this construction and a simple
attribution, widely but incorrectly use colons in place of commas, as in
this erroneous usage: “He voted against it, declaring: ‘The only thing
this bill will stimulate is the national debt.’” In this case, or after
“He said” or “She asked” or a similar term, a simple comma suffices.
Introducing a List
When a phrase that introduces a numbered, unnumbered, or bullet list,
or a run-in list, syntactically comes to a stop, use the colon as the
bumper:
“The two central questions in ethical theories are as follows:
1. What is the good for which we strive or should strive, and what is the evil that we would like to or must avoid?
2. What is the proper or desired course of action, and what is the inappropriate or forbidden course of action?”
But when each item in the list is an incomplete sentence that continues an introductory phrase, omit it:
“For this experiment, you will need electrical wire (at least 3
feet), a pair of wire cutters, a battery, a flashlight bulb, and
electrical tape.”
When, in the latter example, the list is formatted with the
introductory phrase and each item on its own line, “For this experiment,
you will need” remains bereft of a colon, and each item ends with a
period.
(Notice that my explanatory introduction to each list type above is closed, with a colon.)
Colons are used in several other ways to clarify relationships
between words and numbers: They set off a character’s name from a line
of dialogue in a script; separate titles and subtitles of books, films,
and other works; distinguish between chapter and verse in reference to
books of the Bible and in similar usages; and separate numerals denoting
hours, minutes, and other units of time.
In addition, they have specific functions in mathematics, logic, and
computer programming, as well as informal roles in setting actions or
sounds apart from words in email and online chats (much as parentheses
are used in quotations and dialogue) and as a basic character in
emoticons (arrangements of punctuation marks and other symbols to
simulate a facial expression).
But it is when the colon is employed in one of the three primary
purposes that errors are most likely to appear and communication is most
likely to be compromised.
From: Daily Writing Tips