Talk to your parents about your plans to write a memoir and ask them if they would like to participate. If so, schedule an interview well in advance to ensure you will have time to complete the entire process.
Break your interview up into chunks if it needs to last more than a couple of hours. It is much easier on both you and an interviewee to limit sessions to one or two hours at a time.
Create a list of questions that provide information specific to your parents. Include basic information such as name and age, but also include questions related elusively to your parents. For example, your parents earliest memories of your personality, strange childhood events you may not remember, and how your parents went about having children are all interesting topics to explore. Create separate lists for both your mother and father using information you already know about each.
Make a list of difficult moments in your life or decisions your parents made that you didn't understand. Interviewing your parents and getting their perspective on actions that may have hurt or confused you can often bring closure and relief.
Set a tape recorder out to capture the answers of your subjects. When you record interviews, you can go back and listen to them later for inspiration or reference help.
Take notes during the interview process of things you would like to further research or follow-up questions you would like to ask. Take notes with a pen and paper, as a laptop or digital device can upset the balance of the interview.
Recruit a neutral third party to interview your parents about sensitive topics if you feel the need. It may be easier for your parents to discuss difficult moments with an impartial observer than someone to whom they have a deep personal connection, especially if the events in question somehow involve you.
Listen to your recordings and check your notes to find new ideas to explore. It's best to interview your parents while they're relatively young, providing you ample time to explore each avenue of thought and discover new memories and experiences along the way.