Step 1) Listen to their opinion and do not interrupt them. The first step in changing someone's mind is respect--if not appreciating--someone else's opinion. Listen before you talk is the first step in changing someone's mind. Don't force your words onto anyone--this doesn't work!
Step 2) Tell them how much you understand their stance and how much you trully appreciate them taking the time out to articulate their stance to you. Higlight the particular strengths in their stance and underscore the weaknesses in their argument. This will open them up to listening to you.
Step 3) Tell them in a very calm and clear tone what you believe. Insert complimentary phrases about their stance within your own argument. This 3 step method often changes people's opinion. If it doesn't change their opinion, the person will like you more for being so complimentary.