You can find interviews through the database Seeker. Seeker searches for content in books, journals, magazines, and newspapers. The best way to do this from the basic search page is to search for the person's name and also the word "interview" as keywords.
If you're on the Advanced Search page, you can also use the person's name and the word "interview" and select "SU Subject Terms" from the drop-down menu next to the search field. This will get you an even more relevant set of results.
You can find audio files of interviews with various authors, artists, public figures, and everyday citizens on NPR's website. If you're looking for a specific person, type the person's name and the word "interview" in the search field on the top right of NPR's homepage. If you're looking to browse interviews, three good shows to look at are Fresh Air, The Diane Rehm Show, and This American Life.
NOTE: Many of the online News sources have links to transcripts of their content.