How do you cite an author within another authors work in APA style Like if Author A talks about Author B in his paper how does one cite author b?

If you are referencing another author cited within the work (secondary source) and you didn't read the work of that author, you would use the same principles as the other citations on this page, but add "as cited in" to the reference:

Brown's work on the APA style (Brown, 1995, as cited in Smith 2005) shows us that ...