Semi-Colons

Use #1

The most frequent use of the semi-colon is between two complete sentences. It can substitute for a comma plus a conjunction. Joining sentences in this way shows the reader that you see a very close relationship between the two sentences.
Example: Tom ate breakfast with his family, and then he left for his trip.
Example: Tom ate breakfast with his family; then he left for his trip.

Do NOT use a semi-colon with a conjunction; use it with a conjunctive adverb.
Example of INCORRECT usage: Tom ate breakfast; and then he left.

Use semi-colons before (and commas after) conjunctive adverbs that come between two sentences.
Example: Unemployment was down; consequently, the stock market surged.

Do NOT use a comma before conjunctive adverbs that come between two sentences.
Example of INCORRECT usage: Unemployment was down, consequently, the stock market surged.

Remember to make sure there is a COMPLETE sentence on BOTH sides of the conjunctive adverb.
Example: The butcher started work early; however, he was still unable to fill the order in time.
Example: The butcher started work early; he was still unable, however, to fill the order in time.

Note
If you want to use the conjunctive adverb for two sentences that are not joined, use a comma instead of a semi-colon.
Example: Almost everyone in the neighborhood were invited. The butcher, however, was not included on the guest list.
(This is only one sentence, there is no semi-colon here.)

Conjunctive adverbs include

Use #2

The only other use for a semi-colon is between items in a series containing internal punctuation.
Example: We moved to several different locations: Barnesville, Ohio; Duluth, Minnesota; Syracuse, New York; and Falmouth, Maine.
(Notice there is a semi-colon before the and.)