Be confident, be assertive, be kind. You are presenting yourself to others and the intent is not that they understand everything about you but that they accept you and treat you with respect.
Be frank and direct: “I am transgender which means that I was born one gender, and I identify as another. Please call me [insert preferred pronouns and name]! Thanks!”
And if you want to invite them to ask you questions, you can do that, too. (I always do.) I think that this can often helpful. It allows people to feel like this isn’t something strange or a “red-zone”/dangerous topic – it’s just another conversation. But if you do open up the floor for questions, you must be aware that people don’t always understand. They are ignorant – a lot of people have absolutely no prior reason to understand or know anything about trans* people or related topics. So you might have to educate them and realize they’re not always (although, sometimes they might be) trying to be rude or mean. They just don’t get it. And with that, maintaining a kind and assertive attitude is crucial (at least in my experience.) If you start attacking them or getting super angry or defensive, they’re going to shut down and not hear you and you’ll lose the opportunity to educate them. Of course if you don’t want to let them ask questions, you have every right to refuse to answer or ask them not to ask you.
Lastly, time is key. People need time to process information you give them, especially if it conflicts with their previous view of you and of the world. You have taken (most likely) a long time to think about your gender and your own identity and how you see yourself, so give them some time to think and to process. Yes, some people will never understand and some people are just straight up assholes, excuse my language. And you can’t change everyone. But time does heal a lot of wounds and it helps a lot of people understand.
I don’t have a ton of advice here because I’ve always been really upfront with my parents and I pretty much tell them everything, but here’s something I learned from a trans support group. For parents who are testy or not completely supportive, tell them that this is something big in your life. Present it with confidence and security and happiness – you have discovered a part of your identity and that is really fantastic. Knowing yourself is really incredible and you trust them enough to share it with them. Tell them this – tell them that you are sharing this pivotal moment in your life with them and you really want them to be a part of your life, to share this amazing piece of your life with you. Parents don’t typically like to miss out on the good things in their kid’s life. So presentation can be key.
At school and with teachers…
I would recommend sitting down with a principal or head teacher or someone of that sort to help you talk through possible options. I think broad information dispersal is best – either by email or a teacher meeting. And in either of those, being frank and direct and asking for respect (by calling you the right pronouns and name) is crucial. See “In general” above.
With younger kids….
Be simple. Little kids don’t really care much about gender. At some ages (5-8 or so) they are testing boundaries and might try to push your buttons at first because some little kids like to make fun of everything and do everything they’re told not to. But for the most part, kids are quick to understand. They don’t have much reality and experience to go off of and so that benefits you because you get to create some of that for them. When I told my little cousins (5 and 10) I told them that some girls were born with boy bodies and some boys were born with girls bodies (yes, not entirely politically correct but bear with me) and I was a boy born with a girl body, that’s all. And they were like “Okay. Wanna play minecraft?”