Make a list of questions about your subject and the event you have been asked to help them write about.
Set up your audio recording equipment as a source for later reference, and start it recording during the very first session. If you have multiple meetings, start and stop the recording device at the beginning and end of each session.
Begin discussing the questions and their answers with your subject, taking notes to supplement your recording.
Spend as much time as possible talking to your subject and getting to know his particular turns of phrase. Lay out your plan for the shape of the piece you are writing, and discuss this with your subject.
Draft your notes into an outline that encompasses all the topics you and your subject discussed.
Review the outline with your subject and take their ideas into consideration--after all, it's their story that's being told--not yours.
Write a first draft, in first person ("I," "me") of the material your subject has given you. Note where you have questions or where additional discussion might be required.
Review your draft with your subject, asking questions to clarify any points that you feel need more explanation.
When you and your subject have agreed on the quality of the piece and the ideas that it communicates, you will have a piece that echoes the sentiments your subject would have put on paper if he had the inclination and ability to write on their own.