How should I use quotation marks in sections of multiline dialogue?

When you are quoting multiple paragraphs, closing quotations go only at the end of the entire quotation. Beginning quotes should be placed at the beginning of each paragraph, though; otherwise it would be hard to tell at a glance that the quotation was still ongoing.

Common Errors by Brians (one of my new favorites) says it this way:

When quoting a long passage involving more than one paragraph, quotation marks go at the beginning of each paragraph, but at the end of only the final one. Dialogue in which the speaker changes with each paragraph has each speech enclosed in its own quotation marks.