Always say you want to record the interview. Do this when setting up the appointment and when you sit down with the interviewee.
Once the interview begins, listen for surprises. If you're prepared, you shouldn't have to think about your next question.
Ask short questions. Lengthy ones risk confusing your guest.
Avoid questions likely to result in one-word answers. Ex: Do you plan to run for re-election?
Questions that begin with "How" "What" or "Why" are most likely to get in-depth answers. Ex: What makes you the best candidate for state Representative? or Why do you want another term in office? or How will you make the case to voters that you are the best candidate?
Avoid the two-pronged question. Ex: Should the administration take a more aggressive stance toward ISIS, or should they let the Iraqi and Syrian governments take the lead?
If your guest gets abstract, wait for her to finish. Then ask for an example.
Don't speak or make noises while your guest answers ("Uh-huh" or "Right.") This could make you sound like you're taking your guest's side in this story. Also it just sounds annoying and may distract the listener.
After your guest finishes, pause for two seconds. This prevents you from interrupting them if they're not finished. Also, they might add a little emphasis or they might start again with a more informative answer. (People are hard-wired to fill silence). Obviously, this doesn't work for a live talk-show interview. But it's perfectly fine for a recording session where you can edit out spaces between your questions.
(During a difficult interview) If your guest responds to your question by not answering the question, ask it again. If your guest gives a similar unsatisfactory response, move on to the next question. Then return to the same question, perhaps rephrased. If your guest refuses to give a satisfactory answer, then you've done your duty; you've given her three opportunities. Listeners can make their own judgments about the response.
Maintain eye contact. This tells the interviewee that you're interested.