What are "Chicago style" citations?

The Chicago Manual of Style allows both parenthetical citation (author-date style) or footnotes, although parenthetical seems to be preferred. Has you teacher recommended a particular style book? If so, follow that. If not, the first link below will take you to the resource I use when my copy of Chicago isn't handy. The second link is to the Q&A on Chicago Manual of Style site. The manual itself is only available to subscribers. If teachers are requiring the style, you might ask the librarian if your school subscribes.