Review your notes and eliminate any extraneous or irrelevant exchanges. Though your "job" requires you to dutifully note the interview word for word, you do not need superfluous exchanges such as, "Would you like some water?" and "No, thank you. I have a water bottle right here."
Review your written notes (if you did not tape-record the interview) to ensure that you know exactly what the interviewee said at every turn of phrase. Now is the time to call the interviewee and ask for clarification or elaboration. (Note that such additions should be indicated in the text as taking place after the interview.)
Consult with your supervisor, teacher or colleague as to what extent, if any, you should play the "language custodian." Most people are prone to careless verbal slips; many more drop the "g" at the end of words -- as in, "I'm goin' to get an ice cream cone." You may rightly decide to automatically add the "g" in cases like these, at the risk of making your subject appear inarticulate or unintelligent. However, if your subject makes repeated and telling verbal assertions -- as in, "I'm goin' to get me an ice cream cone" -- you may decide to leave his words unvarnished -- to capture the subject's personality and speaking style.
Write a compelling introduction that sets the stage properly for the interview to follow. In a wide-ranging interview -- say, one that covers someone's 20-year career -- provide the reader with an overview and some highlights of the interview to follow. You may also want to include where the interview took place, what the subject was wearing and any other personal details that will truly help put the reader "in the moment" as he reads the interview.
Set up the format of the interview so that it is clear to the reader who is speaking. If you are representing an organization, it is customary to put this name -- not your personal name, such as "Jim" or "Nancy" -- as a preface to the question. Likewise, it is customary to use the interviewee's last name as a preface to the answer. However, use the subject's first name if this style appears too formal. You may also choose to set the questions and answers in different type styles -- say, italic font for the questions and regular font for the answers. This decision is purely a matter of personal preference.
Keep your "custodial mop" in hand as you transcribe the interview, being careful to use ellipsis for word or words you decide to eliminate (say, if the subject rambles or goes off-topic). Remember that you are quoting someone word for word. So you, in turn, must be especially judicious about transcribing the subject's words accurately and with precision.
Consider extending a kind gesture to your subject if you discover an obvious faux paus. For example, if your subject says, "The tension in the room was absolutely palatable," you could rightfully follow that word with "(sic)," which indicates to the reader that the mistake was the subject's, not yours. The subject obviously meant "palpable," as it's highly doubtful that the tension in the room was edible. Simply substituting the correct word under such conditions is considered part of the "gentlemanly art" of writing up interviews.
Write a conclusion, knowing full well that this is usually the trickiest component of an article. In the case of an interview, however, when a subject has been "exposed" and a reader may think he has heard it all, a fitting conclusion might contain an element of surprise or the unexpected. Barring that, if the subject has repeatedly returned to a theme or a topic throughout the interview, the conclusion might seize upon that element and attempt to tie the theme together.