Q. If the author cites a source, and I use that information, do I cite the author or the source the author cited?

If you're able to find a copy of the original source, it is usually best to do that in order to verify the information and then cite that author directly.

However, if their original work is not available, you would cite the author whose work you did read (the one that cited the original source) in the reference list and then reference the original author in the text.

This page has an example of how to do that in APA style, while this page shows an example in MLA style.