It's quite normal to keep your writing ambitions hidden for a while. Don't be afraid to become more vocal about it eventually though, even before the first dollar/pound/euro is earned.
Family is obviously an important first step. Support and motivation from loved ones can be extremely helpful.
When I visit my grandmother and she asks about the book I'm working on (by which she means screenplay, she's just not quite sure what the difference is), and I have to stay vague in my answer because I barely made progress since the last time I visited her, that always gets my butt in gear again.
Once at the stage where you feel comfortable enough about your writing to send your work out into the harsh world, it can be helpful to be more open about your goals and dreams, to anyone who will listen.
It took me a long time to take that step, mentally, to call myself a writer instead of a wannabe writer. But once you do, it helps to keep you motivated and to keep going through tough moments. Much harder to throw in the towel if it's not just your family who know what you're up to - because they'll love you no matter what you do - but also your friends, neighbors, vague acquaintances and that cute girl at the supermarket checkout. If you give up you'll be a failed writer, so you have to keep working hard.
Sure, you may get the occasional poorly disguised look of pity - especially when your answer to their questions starts with "nothing yet, but..." You get used to those pretty fast though, and you get as least as many positive reactions.
And once your writing career does get off the ground, the looks on the faces of the unbelievers will be much more memorable if they've considered you delusional for several years.
