ok, advice.
Advice is hard to give, but let's try.
I would tell any good friend first, to have backup, you know? Then ask your mom if she's got a minute. Sit her down and tell her. Don't tell her words she wouldn't understand, you don't have to say "trans" either. Just tell her how you feel and what you want to do about it. Start easy on her like with binders, and don't go like "I want top surgery"

Now, so much for your part. She may freak or something. If she does, just leave and stay out a few hours with the friend you've come out to. Don't take any ->-bleeped-<- from anybody.
If she acts weird, let her. She needs to come around, right? She will need a few weeks to get a grip. She deserves that time, too.
So next you should talk to your dad- Or you talk to him first. Do it the way you feel comfortable. But make sure you got backup to go for pizza and a movie just in case your parents freak.
How long have you known you were a guy? And how old are you?