I am reading an article and in the article, it cited another author. How do I cite this? Do I cite the article I'm reading or the other person?
It should depend on what information you are citing. If someone else cited the information from the other source, you can probably find their source at the end of the article and then use that. However, if the information that you are providing builds upon the source information, you should cite the second article. If it's still unclear, consider citing both and be done with it.
Ideally, you should try to get a hold of the original source. (If you have difficulty finding it, go to your library as they can often get things through ILL (Inter-Library Loan)).
If it's out of print, or in a language that you don't speak, or for whatever reason you really can't get it to cite, you should use the phrase "as cited in" and reference the "secondary source" (the one you actually read). As an example from APA :
Allport's diary (as cited in Nicholson, 2003).
I have links to how to handle indirect citation in other citation styles on the Academia SE site