Face to Face
If you have the opportunity to meet face to face with your family member, this is usually the best option. It offers the opportunity for a comfortable environment, back-and-forth participation, video recording and the personal touch that is so hard to achieve long distance.
Send an introductory letter or email to create a rapport with your relative by telling them about yourself, your family and why you are so interested in the family history. Follow this up with a list of open-ended questions. You will find this usually results in a much better response than a letter saying "tell me everything about the family" or a list of fill-in-the blank questions. Increase your chances of a reply by including a self-addressed, stamped return envelope.
Email is a wonderful invention which can be successfully used to collect oral histories, but you will also often find that is is something which many of your relatives, especially the older ones, don't trust or don't have access to. If you have a family member who loves email, then by all means use it, but don't expect to gather much useful information that way from someone who seems reluctant about the whole process.
Phone interviews can be tough, especially when you are interviewing relatives you hardly know, but they also offer the back-and-forth exchange that you can't easily achieve through the mail. A phone interview is also a practical way to reach relatives that live too far to justify an in-person interview, and can also make it easier to collect information over an extended period of time.
Be prepared for a bit of gruffness when calling distant relatives who don't know who you are. They may not trust your motivations. Here, an introductory letter followed up by the phone call may do wonders.