What's the correct way to cite a paper cited by another paper?

In APA style, you can write, (e.g., see this APA tutorial)

Featherstone et al 1900 (as cited in Thomas and Cullen 2002)

Of course, in general you should try your best to read the original and cite the original directly.

Someone in the comments asked:

"In such case do I need to list original paper also in reference section or only the recent one I am referring to?"

The reference to the original article is the more important reference to include, but you should include both in your reference list.

The following is with regards to Chicago Style as of 11/25/2018 14.260: Citations taken from secondary sources Chapter Contents / Special Types of References / Citations Taken from Secondary Sources To cite a source from a secondary source (“quoted in . . .”) is generally to be discouraged, since authors are expected to have examined the works they cite. If an original source is unavailable, however, both the original and the secondary source must be listed.

If you are using a quote from author A that author B is citing, you would go ahead and use the quote from author A and cite it like this:

Blah blah, blahblahblah, blah blah blah-blah blah (qtd. in Author B 65).