I told my parents by email (I live halfway around the world from them), and my immediate family and coworkers in person. Everyone else got my new name at most when I next met them – they’ll figure it out, or not, in their own time.

I suggest:

• say what you are doing (eg, “I am going to live as a woman from now on”)
• say what you expect of them (eg, “I’d like you to call me Twilight Sparkle”)
• then shut up and wait for a response

And if you’re not expecting it to go well,

• don’t try to justify it
• don’t argue
• don’t bargain or downplay it
• be prepared to just leave

Good luck!