I'm a veggie and have been for about 12-13 years now since I was in grade 6.
I really do honestly think its a healthier diet in a lot if ways and there is new research now that suggests it's on par with the Mediterranean diet that is known for being healthy. BUT. You have to be prepared to put a bit of work in to start with.
A lot of the time it's pretty easy to substitute something for meat. Beans, mushrooms, meat substitutes like quorn, tofu eggs etc (if you like that kind of thing).
I find it easier to go through a few cook books or taste.com.au (I'm the veggie section) once a week and plan three or four things I'm going to make. Do the shopping for those and try to keep an eye on what eating the rest of the day. That way evertyhing is still fresh when you cook it :)
It's important to try to vet a variety of veggies to get the different nutrients from all of them and try to slip extra ones in where you can for a boost. Like banana on your peanut butter toast.
I would suggest investigating online first. It is an adjustment but it becomes second nature after a whole. Getting a blood test every six months or so as well for the first couple of years is a good love too to make sure you're getting what you need.
Let me know if you need any help or meal suggestions etc :)