How can I get birth control?

E • Animal lover, artist, & wannabe chef. 18/CA 🦋💗🐺✨♏️
Hey everyone, I'm sixteen and I would like to get birth control, but I have no idea how to talk to my parents (I live with my dad and stepmom, and I really don't feel comfortable talking to either of them about it). I would like to make my own doctors appointment but I would need to talk to my dad about that because since he gained full custody my insurance got all messed up. 
Ideally, what I would like to do would be to go to my doctor (or even an obgyn, but I've never been to one before) and talk about my body and what would work best for me. I would also prefer my parents not to know that I'm on birth control - just because my sexual life is something I'd like to keep more private. 
How can I either talk to my dad or make my own apppointmens???