The most important question I always ask about this type of situation is, "Do they need to know?" Is it something that is very pressing for one's health and well being that merits the risk of this type of reveal to others. Because it is very, very much a risk. If the answer is anything short of something along the lines of, "It is really bothering me and distracting me. I can't get my mind off of it. I feel like a fake and that I am always hiding, lying to everyone about who I am." It is generally not a good idea to share any more than people need to know. Although, if they do need to know, there is a level of tact one should employ with that - coming out of the gate in a sit-down conversation about how one is "X, Y, and Z" is not going to go over very well unless one has an exceptional relationship to that person and can speak on a really deep level with them and them take it seriously.
So this leads into the means of approach, which I simply say to be vague with and careful. Good examples are reincarnation, the idea of afterlife and past lives, totems or animal spirits, and really never spelling it outright to people. I say this because one has to ease their way into the waters of what people do understand rather than diving deep into what they do not. Generally, people are accepting of the idea of reincarnation and past lives and the like and when it comes up in conversation, sort of explaining feeling like one has been here before and how different the world was or is, and how there are still certain attachments to things and so on is a safer way about it. I have found fairly consistently people make their guesses in private as to what was said and make some assumptions but never leap to the kind of overreaction that comes with the "otherkin explanation", so to speak. There is a certain stigma attached to it and much of avoiding it is not just knowing oneself beyond a shadow of a doubt but then presenting it in a marketable way. Gender explanations are probably best kept the same way, sort of giving bits and references to things rather than spelling the words out for people such as by claiming a label; that evokes a certain immediate, unavoidable prejudice, right or wrong.
You know your family better than we do. Some families will accept you no matter what, while others may freak out and take some kind of negative action. What kind of people are they? Do they seem accepting in general, or do they make mean comments about others who are different? Are they open to alternative spiritualities or genders? Or will they send you to an exorcist or a camp? Where do they fit on that scale? If it's closer to the second one, I'd recommend keeping it to yourself. If they are generally very supportive and might help you then maybe consider whether or not telling them will be helpful to you or not.
I agree with Red in Tooth about feeling out the situation before diving right in.