If your child came out to you, how did you adjust?

One of my children is questioning their gender, and they seem at ease with non-binary. I found this out yesterday, so I'm approaching this gently, though I feel ill-prepared. I want to be who they need.

I'm curious about the experiences of other parents, or stories about your parents learning to adjust if you came out to them.

Follow-up: Thank you all so much for your stories and your feedback!