Please hang out here! This is a big part of why it exists (IMHO).
Props for having a level-headed initial reaction. Next thing to do is to educate yourself and you're already doing that! I have a good feeling about you.
PFLAG. (http://community.pflag.org/) It's a good jumping-off point for those completely new to this idea and may be helpful to you both. Also spend some time on wikipedia if you're interested in the history behind gender identities, gender nonconforming people, third genders, philosophies on the role of gender, psychology of the origin of gender, actual experiments on people to test theories of gender, etc. Personally I learned everything I know now on wikipedia and subsequently found my place in the mess by talking to people here and a few close friends.
If you're comfortable with it, offer to spend a little time going through this information-gathering process with your sibling and ask questions along the way about how they feel it applies to them. If not, they may still appreciate the chance to talk to you as they figure themselves out, even if this way they explain it to you at each step. When you (both) get around to it, you can ask whether they'd like to be called he or she, sister or brother, when it's just the two of you and around other people. (Side note: there are other genders but your sibling sounds like they already have one in mind and the difference would be whether they want to be known to everyone as a boy or a girl.)
It is definitely relevant that your parents seem like they would be supportive. I'm honestly just floored that this is starting to happen. I had to convince mine that my feelings and my proposed solution/explanation matched, that it should make a difference if they recognize and honor that, etc. and while it wasn't the kind of reaction of disgust and disbelief I expect from certain extended family members (whom I have told nothing), it was not simple. Your reaction gives me so much hope. If your parents react similarly, this may be a relatively painless period of exploration for your sibling.
Thank you for coming here. Please keep posting if you have further specific questions or concerns!