Let's be clear winning an argument is not easy... in fact even if you win the face to face contact of the argument you don't really win because the other person will likely resent the fact that you where right and they were not. Some people will be grateful that you showed them the errors of their ways but some small part of them will always wish you were wrong and they were right.
The best way to win an argument is to not engage in one in the first place, but if you must engage and you are right then just let the other person win anyway. Now this may seem cruel or uncaring to allow people that you care about to go through the rest of their day, week or life with a mistaken idea of how things truly are but if you really care about them you will still want them in your life and that is the best way to keep them. And if you don't care about them then why does it matter what they think or believe. The time spent arguing is time lost that you will never get back.
Here's is what you do to get them to your way of thinking without engaging in an argument. After the subject has been discussed and you let them continue with their current thoughts, you simply go out and prove that your stance on the subject is the correct one. Evidence or proof that your idea is the correct one is a much strong "argument" than verbal combat. Once you have proven your point, say nothing... no "I told you so"... "see you were wrong"... "see I was right". The facts will always win out and eventually the person you were trying to show the facts to will find them on their own.