How do I become a vegetarian? and what is the difference between vegan and vegetarian?

I have had a very difficult year and have a need to make some minor changes. I have been getting back to my spiritual roots by meditating, having started yoga, and getting back on an enlightened path. As part of this, I am contemplating turning vegatarian. Everyone I know who is vegetarian is so healthy, and I have a need to do the same. Can someone give me good tips, sites and tell me the difference between vegen and vegetarian? I am also a single mother who is a fulltime student, therefore on a serious budget, so budgeting hints for this endeavor would be greatly appreciated! Thank you!