Ah, the semicolon. Perhaps the single most misused of all its kin. Here are a few of the basics for semicolon usage:

Use a semicolon in place of a period or conjunction to connect two complete sentences. This is particularly useful when you want to show a direct relationship between the two thoughts without the added beat of a conjunction or the full stop of a period.

Example:  The door clicked shut behind him; she slumped on the couch.

Semicolons are also great for lists. Use the semicolon followed by an introductory word (i.e., e.g., for example, for instance) to set off the listed items in your sentence, which will all be separated by commas.

Example: I need a few things for dinner; i.e., onions, garlic, parsley, and walnuts.

You can also use a semicolon to connect two complete sentences that are also joined by a conjunction when the first sentence contains one or more commas.

Example: After the breakup, he was devastated; and that was really all they saw anymore.