Looking through a newsletter from my publisher, Wheatmark.com, I discovered a free radio booking resource called Radio Guest List. Once you sign-in with them, they send out a daily listing of radio outlets requesting guests to interview for a wide range of topics.
Depending on the program's target audience, they are looking for authors, musicians, lifestyle commentators, financial planners, and "experts" in many areas. This website simply lists stations that need on-air talent. Once you find a request for a quest spot that is in your area of expertise, you contact their booking agent. That's it!
If they are interested, they will email you back to make arrangements. Within a week, I have been booked for two interviews to discuss my novel - Zug Island - one is for a show called Beef Stew, and the other is for a program named Sayin It Plain.
Other than readers, what new authors desperately need are publicity and exposure. This website provides both for free. Take advantage of it. Good luck!