well it all depends on where you are right now with meat eating. I'd say stop with red meat then move on to chicken and so forth. I've been a vegetarian for almost 14years now, and I honestly just quit eating meat "cold turkey". haha no pun intended. However, being a vegetarian doesn't automatically = healthy. It's a lot cheaper to live off pizza and grilled cheese than cooking vegetarian meals. Because I don't who this is, I don't know what your kitchen habits are like. In case you aren't a kitchen wiz, just make sure you're ready to do a good amount of cooking if you don't want to live off pasta and melted cheese. Also, there are a lot of really delicious meat alternatives from brands like MorningStar, but because they're frozen they're very high in sodium. So you don't want to overload on those too much.
The great thing about becoming a vegetarian now is that there are so many blogs, books, and magazines to embracing the lifestyle. A million more resources than when I started out. So, just do some research, pick out some recipes that sound good to try and start infusing them into your weekly eating schedule.

WOW. that was a lot. I hope it helps! :)