There's only one way for them to find out; you gotta tell them. That is of course being under the impression you want them to know. Avoid arguments, answer any questions they may have and most of all, speak with confidence. If you intend on convincing your family this is who you are and what you need to do for true self-happiness, it needs to be told with the utmost confidence and assurance. Any doubt they sense in you may alter their view on the subject. And while that doesn't make it any less true, obviously you want their support. Best of luck!