Chances are you'll have to wear two hats: director and interviewer; but to simplify the subject, let's separate these functions.
As director, watch for angle changes. If the interview lasts more than a couple of minutes, you'll need multiple setups for variety. And if you use the subject-only style, they re an absolute must for cutaways. When you are choosing alternate angles you have two options:

• Zoom in place to create, say, a medium shot, a head and shoulders closeup and a closeup. The advantage of this method is speed: you can frame a new angle instantly and you don't need to change your lighting set up. The disadvantage is that a change in image size creates a mild jump-cut.
• Move to a setup at, maybe, eight o clock, while zooming to change image size. This creates a smoother cut but it interrupts the interview's flow while repositioning the camera and, perhaps, re-adjusting the lights and mike. If another edit is necessary you'll have to move again.

Frequent edits will indeed be necessary because no interview can be goof-proof. As director, you must watch for every single thing that will have to be cut and then cover the edit with an angle change. At a minimum, zoom to a new image size each time you see the need for cutting and make sure that the interview pauses while you re-frame, so you can cut the zoom out later.
If the interviewer appears on camera, collect all-purpose cutaways of him or her listening intently, nodding sagely and smiling in appreciation. Your editor will bless you for it.
If your setting allows it, try to get a view of the subject, shooting over the shoulder of the interviewer. This puts both people in context by showing the spatial relationship they have between them.
Now switch to your interviewer's hat. The key here is asking open-ended questions. "Were the winters cold in Dubuque?" "You bet!" That question is DOA. To revive it, try, "Tell us about the winters in Dubuque." Now you re off and running.
And you should run with follow-up questions: "Talk some about the snow." "Tell us about winter activities." And follow-ups to the follow-ups: "Did you prefer sleds or toboggans?" When your promptings are finally edited together, the result might resemble this:
Well, those winters were cold enough to freeze the beak off a buzzard. We kids d stay outdoors as long as we could stand it. Course there wasn't much packed snow for sledding, but I ran my old toboggan down some mighty scary hills!
While you re asking all those questions, don't forget the most important thing: look interested and encouraging. Even if you re distracted by directing and videography, show the subject that you care. It's the surest way to obtain good results.

When it's time to edit those results, the main trick is to use multiple angles and cutaways to hide the cuts needed to drop mistakes. There are other things you can do to edit a snappy interview (particularly if you re doing computer-based post production).
First, if you used different mike positions, you may need to equalize and balance the sound quality from the various setups. It's easier to do this with long, uncut takes than with short pieces of edited shots. So do as much sound processing as possible before you start editing the show.
Next, remember that an interview is audio-driven: it's a sort of illustrated radio show. For this reason, use the sound to set the pace (hint: listen to each edited sequence with the picture off). If the audio is brisk and smooth, you have a good pace.
No matter how well you ve directed the shoot, you'll find places where a cut's essential but there's no cutaway. When this happens, use a digital video effect (DVE) to frankly admit a time lapse. A fast, soft-edged, wipe across the screen works well. News Magazine shows like Dateline NBC often use quick dissolves to bridge a jump cut.
Finally, do your best to get material for voice overs. This will help relieve the monotony of a talking head. It might be album snapshots of winter in Dubuque, historical footage of winter anywhere or a toboggan labeled Rosebud. If you look at interviews edited by a master like Ken Burns, you'll notice that half the creativity lies in finding something to fill the screen when there's really nothing essential to show.
So here we are, landed safely on the far side of that interview enchilada. There's more, of course, to getting great video interviews, but perhaps this brief flyover'll reduce a big subject to manageably proportions and help get you started producing your own interviews.