Between my blog and my other writing work lately, I seem to be doing a whole lot of interviews. In some cases, the interviews are for information, such as when I'm working on a news article. In that case I'm probably also looking for some quotes. With others, like the ones I post here, the whole point is to share the interview itself.
I used to hate doing interviews. It wasn't the process, unless there's transcription involved. (More on this topic later, transcription is essentially taking the audio or video interview and writing or typing it out into text.) The bigger problem for me was actually coming up with the questions. What the heck do you ask?
First, preparation. You don't have to become an expert on your topic, but at least learn the basics. That way you not only go into the interview sounding informed, but you can spend your time on issues that don't involve basic explanations or clarifications (unless that's what you need to focus on). Generally you want to establish a rapport with the person you're interviewing, and showing that you respect their time is a huge one (including showing up a bit early, making sure that you're ready, choosing as pleasant an atmosphere as possible, working with their schedule, etc.)
Then, as with anything of this nature, you need to consider the purpose of the interview. For example, are you trying to learn about something that you can then explain to other people? An informational interview can be much different than a personal one. Still, an informational interview can have some personal questions revolving around their personal relationship with the topic. I do this in the freelancer interviews on this blog. See if you can spot where. The point is to bring the subject to life a bit.
Is the thing you're trying to learn about the actual person? Even if you don't have time to learn everything about them ahead of time, at least learn what they're known for, and know which aspect of them your publication is most interested in. For example, Diana Gabaldon is a well-known historical fiction writer but my topic is freelancing, so I focused on her freelance career, which is actually pretty colorful (and is something not a lot of people ask about, so it lets me show a unique side of her others don't focus on).
When you want people to get to know a person, it's important to try to capture some of their personality. Often this is done through carefully choosing some quotes to give the flavor of their speech. Or, in my case, I show the full text of the interviews. Some people do so by describing people's clothing and/or mannerisms, or telling a story about something that happened while talking to this person. The method you choose depends on your publication, audience, style, and goals.
As to the questions themselves, definitely have a pre-prepared list. If nothing else, you can fall back on the questions you wrote down to try to spark more interesting ones. When I'm interviewing someone by email, I'll sometimes say that they don't have to answer every single one, especially if I send a large number of them (I'm a naturally curious person, I can't help it!)
No matter how you're doing the interview (in person, email, phone, IM, whatever), listen for statements that might provide good leaping points toward interesting answers. But for heaven's sake don't interrupt and ask right away. I won't say I'm a saint about this, I come from a very interrupting family, but I do my best to listen far more than I talk when I'm interviewing. If you're like me and have a bad short-term memory, take notes. That lets you jot down a question so you won't forget while still listening.
If time is limited, focus on things that you couldn't learn by just sitting down with a good search engine. Ultimately what makes an interview interesting (no matter what the context) is learning something new. If all you manage to do is rehash what people already know, even if you do it with flair, the result will be disappointing.
And don't be too hard on yourself if the first few are difficult. Doing interviews does get much easier over time. You get a feel for the rhythm and flow and what makes for a good avenue for further questions.
Note: I wanted to add one bit that doesn't entirely belong, but is very important. If you want to record a phone interview (and I'm using the term phone loosely, even if it's over the Internet) the best practice legally is to include you asking them for permission on the recording, and them giving you permission. It's illegal in some states/provinces/countries/whatever to record a phone call without everyone involved giving permission.