The Semicolon
I love the semicolon; it is my favorite punctuation mark. The semicolon can be used between two closely related complete sentences; moreover, it can be used between two complete sentences linked with a transitional word such as also, moreover, therefore, etc. Don’t be confused by the semicolon’s name; think of a semicolon as a hard comma or a soft period, NOT as a colon. It should be called a "semiperiod."
The semicolon has three major uses; I’ve mentioned two already in the above introduction.
Use a semicolon between two closely related complete sentences--i.e., two sentences that could stand alone if separated by a period.
I love the semicolon; it is my favorite punctuation mark.
Use a semicolon between two complete sentences linked with a conjunctive adverb or transitional phrase (e.g.,. however, moreover, etc.).
The semicolon can be used between two complete sentences; moreover, it can be used between two complete sentences linked with a transitional word such as also.
Use a semicolon between items in a complicated series or list that incorporates commas as well; this helps keep it clear what the items are.
WRONG: Among the students at the party were Jeff, president of the Student Council, Norbert, the president of the debate club, and Missy, the head cheerleader. (Note how hard it is to tell where each item ends.)
RIGHT: Among the students at the party were Jeff, president of the Student Council; Norbert, the president of the debate club; and Missy, the head cheerleader.
DO NOT use the semicolon in the following cases:
To introduce a list (use a colon instead).
Between complete sentences joined by and, nor, but, or, yet, so (coordinating conjunctions).
Between a dependent clause and the rest of the sentence.
WRONG: No one applied for the job; even though it was advertised extensively.
RIGHT: No one applied for the job, even though it was advertised extensively.
Because even though it was advertised extensively is a dependent clause (it can’t stand alone as a sentence), it must be separated from the independent clause with a comma, not a semicolon.
The Colon
Think of the colon as an equal sign. It is nowhere near as cool as the semicolon, but here’s what it can (and can’t) do.
The colon has two major uses:
Use a colon after a complete sentence to introduce a quote or a list (as I just did).
Use a colon between two complete sentences if the second summarizes the first (here’s where the equal sign comes in).
Cynthia can't see the forest for the trees: that's her major problem.
DO NOT use the colon in the following areas:
1) Between a verb and its complement or object:
WRONG: The three types of transportation to get to New York are: train, car, or airplane.
RIGHT: The three types of transportation to get to New York are train, car, or airplane.
Don’t use a colon between the verb are and its complement, train, car, or airplane.
2) Between a preposition and its object:
WRONG: I applied to grad schools in: New York, Massachusetts, and Hawaii.
RIGHT: I applied to grad schools in New York, Massachusetts, and Hawaii.
3) After including, such as, or for example; a colon means the same things as these words, and to use the colon is redundant.
WRONG: Cynthia likes fruit, including: bananas, apples, and oranges.
RIGHT: Cynthia likes fruit, including bananas, apples, and oranges.
Source: http://academics.smcvt.edu/writingctr/semicolons.htm