Wow, I don't know if there is an easy way to do this. My family tried it once so I have some experience with that.
I concluded that being vegetarian may not be right for every one. While I believe that it is politically right for every one, that doesn't mean it's going to work for them as a lifestyle.
If I were going to try this again, I would do it slowly. I would make one or two meals a week that were vegetarian, then slowly increase the number over time. I would try to gently educate them - but no nagging or guilt - people change most when they believe it's their own idea.