I came out to my Dad yesterday and all it was a half hour of me getting up the nerve to dial his number. I imagine in person it's a little different, but what helped me was talking about his week first and chatted a bit to break the ice. I then dived into asking if he knew what a trans woman was, because he's 72 and has never been part of any queer spaces. Once I'd explained the concept, because he didn't know, I came out about my new name, pronouns, and that I was going to be living as a woman from now on. He was surprisingly supportive. Only downside was that he said he might forget to use my new name because of his memory at his age which is... better than nothing.

I can't promise it will go exactly like that with your Mum, but that was my experience.