How do you politely ask someone to be on your committee? I'm a graduate student finishing up my first year, and I'm currently in the Master's program but am planning on switching to the PhD program at my university (which is located in the U.S.). I've chosen people I'm interested in asking and my adviser's okayed my selection, but I was wondering how to go about asking these individuals.

What format is appropriate to ask people to be on your committee? Should I email each person, or should I set up a physical meeting to discuss my goals and 'pop the question'?

What should I say in the email/meeting? Most of the potential committee members I'm planning on asking don't know me very well, but they at least know my name (I think). Do I need to discuss why I want them on my committee? How much do I tell them about my project (which is still in the beginning stages)?
I suggest an in-person meeting with each of them, which you can initiate with a brief but explanatory email: "I would like to meet with you for an hour in your office to discuss the possibility of you joining my dissertation committee.  Based on your work and experience in X, Y, and Z, I think you might be a valuable committee member. ".

When you meet in person, you can treat it as a two-way interview.  They should be interviewing you to determine if this is a good match and if they believe in your research topic and approach.  Likewise, you should be interviewing them to determine that they will perform well on your particular committee.  Do they have enough time?  Do they get along with other committee members? How do they evaluate dissertations and the process of writing dissertations?  What sort of feedback or support are they capable of giving you outside of the official meetings? What do they dislike or seek to avoid in the process of evaluating dissertations or being on the dissertation committee?  And so on.  You should also ask questions regarding their future plans, including sabbaticals, possible changes in job or employer (esp. for non-tenured professors), or possible retirement.

These questions that you ask a prospective committee member can help you avoid many committee problems later on.