How do I cite a source from a another source?
Under some circumstances, citing a source inside another source is acceptable. For example, perhaps the original source is not in a language you can read or not readily available. This page describes the APA method for citing using this style. Here is an example that demonstrates how to do this.

For example, if Allport's work is cited in Nicholson and you did not read Allport's work, list the Nicholson reference in the reference list. In the text, use the following citation:
Allport's diary (as cited in Nicholson, 2003).

I would add the caveat one should always try to view the original document whenever possible. I knew a professor in grad school who was added to a manuscript late in the publication process and his name did not appear in the yearly abstract book, but was only included as an author on the original article. He could tell who did not read his article, but only read the abstract book or cited other people because he was not listed as a coauthor in the work cited. For perspective, I was told this story in 2007 and the article was likely published in the 1980s.
This example was possible because prior to online journals and widespread use of search engines, annual abstract and indexes were published (for this professor's field, the practice continued until the mid-to-late 1990s). As noted in a comment, this would be more difficult with the advent of Google Scholar and other online search tools and their corresponding reference manager tools.