Do you live with your parents or relatives? Are you required to cook for them often? Are they big meat eaters? These are questions you should ask yourself before you tell them, so you will be prepared for their objections, and be able to stick to your convictions. Which raises another question. Are you sure you want to do this? Becoming a vegetarian is not easy, especially if you've been a meat eater all your life. You should give this a lot of thought. Do some research as to what you'll have to give up besides meat, such as milk, butter, cream, whipping cream (ouch), ice cream (ouch, ouch), cheese, etc, etc.
Good Luck, whatever you decide.