Anatomy of an Article
The Interview (Q & A, or prose-style)
An interview is kissing cousin to the profile, and may be approached in Q & A (question and answer) format or written in prose form (where it's virtually indistinguishable from the profile — see also). Your task for this type of article is much like that of the profile: you're still aiming at getting an artist's story so you can offer some background and context by which the reader can get at their artwork.
There are a number of advantages to the standard Q & A interview: when it's well edited, this format allows an artist's personality and individual voice to really shine through the transcript. There's very little standing between the reader and the interview subject, and when the questions are insightful and the interview subject is eloquent and candid, reading the Q & A can give the reader a feeling of intimacy akin to sitting in the room with you both as you chat.
As wonderful as Q & A can be, this deceptively simple format is tough to pull off cleanly—especially if your interview subject isn't particularly articulate or gregarious. These sorts of interviews—often edited down from audio transcripts of a conversation—can be awfully hard to shape into something that's pleasant and coherent to read. You'll be surprised how clunky spoken language is when you begin to transcribe from a recording.
Google is your ally
It goes without saying, but a bit of pre-interview prep work is in order before you meet up to talk with someone. Read other interviews your subject has given if they're available. Visit your subject's website, find out about their work, their history. See what personal details catch your attention, what things leave you curious to know more. Start framing your questions around those. Prepare a list of questions that you'd like to ask about. Be sure to hit enough background questions to elicit sufficient introductory information from your interviewee that your readers will have a good place to start from.
See the artist's work in person if you can
If there's a show to see, see it. If you're allowed a sneak peek at a performance or exhibition, take it. If an artist invites you to their studio, and you're going to be writing about their work— take them up on the offer and go there. There's no substitute for encountering an artist's work in person. And that experience with the work will translate into a sense of immediacy and easy familiarity when you write about the artist.
Now, unshackle yourself from your prepared questions and really listen
One of the main advantages to doing good research and preparing questions ahead of time is that you gain enough familiarity with your subject, their history, and work, that you have confidence about what you'd like to know more on going into the interview. Often, you'll find that such prep work and a list of questions has given you enough confidence, once the conversation gets started, that you may not need to refer much to your prepared prompts. Try to have an actual conversation — not just a series of pre-set questions and answers: respond to what your interviewee actually says.
Cutting it down to size
Don't try to transcribe the whole of a recorded conversation. Instead, as you're listening to the recording, narrow your attention to those questions and answers that are most articulately expressed and with the most compelling insights to share. If you're judicious about what you put into text form, and transcribe from the beginning with a narrative arc in mind, the editing and cutting process when you try to shape the interview into an article with a beginning/middle/end will be much easier later. Feel free to eliminate ums and ahs, and keep an eye out for repetition.