It can be a little frightening to transition to a veggie lifestyle when you're still living with your parents. I was fifteen when I became a vegetarian seven years ago, and my mother was very upset in the beginning. Here are a few things you can do to calm your parents down:
1. Explain to them why you want to become a vegetarian. Have you always loved animals? Are you concerned about the environment or your health? Many parents are proud of their children when they express articulate opinions about the world around them, even if the viewpoint differs from their own.
2. Research vegetarianism on the internet together. There are many good sites to take a look at, though I would recommend avoiding information from radical groups like PETA. Most parents aren't receptive to their style. Check out nutrition sites, sites about the way animals are treated in the meat industry, etc. If your family is religious, many religious groups also have information on the spiritual benefits of being a vegetarian.
3. Decide what sort of vegetarian you want to be. There are many different kinds. The traditional vegetarian is called a lacto-ovo vegetarian. They don't eat any meat or seafood but do consume eggs and dairy products. Pesco-vegetarians don't eat red meat or poultry but do eat seafood. Vegans, on the other hand, don't eat any products that come from animals, including eggs, dairy, and even honey. Once you know what your diet will be like, you can research ways to stay healthy and get all the vitamins you need. Many parents worry about how their vegetarian children will get proper nutrition. Discuss meals and vitamin supplements with them to make them more comfortable.
4. Ask you parents what, exactly, is concerning them. My mother was upset because she felt sure that I would never be able to eat with the family again. Once I reminded her that many of our traditional family meals were or could easily be made vegetarian-friendly (like most pasta dishes, pizza, etc.) she felt better. I also made a habit of eating the side dishes my mother cooked for the family and just substituting a soy product for whatever meat they were eating. Morningstar Farms, Boca, and Gardenburger offer a wide variety of frozen, protein-rich products you can substitute for meat.
5. If you are sixteen or older, offer to get a job to help buy groceries. If your family doesn't normally purchase vegetarian-friendly food, it can be expensive for them to get their normal groceries in addition to tofu, fresh veggies, hummus, Boca burgers, and all of the things you will need to keep a healthy diet. They might be much more amenable to the transition if you offer to take responsibility and pay for some of your own food.
I hope this helps. Every parent is different, and their concerns may vary. Just talk to them openly and honestly and think of ways to deal with their specific worries. Most importantly, DON'T FIGHT. They'll respect you and your decision more if you approach the problem calmly and rationally and don't lose your temper.