But I think to be really believable, there has to be just enough of the real world in there to 1) keep your readers interested and 2) give them something to relate to. So, you know, it's a tricky balance. You've got to leave enough to be recognizable, to hold their interest and to gain your readers' willing suspension of disbelief. But you've got to give them enough to make it fun.
Another question: if your character is from "our" world and introduced to this new world, how long do you give them to accept the rules of the world you've created? Personally, my thinking is the less time you spend farting around with this, the better. Especially with kids. Give them a page or so of doubt, and then get on with the story. Harry Potter would have been a totally different book if it took Harry three books to accept magic was real ... (a totally suckier book, btw).
My favorite way, of course, to do this is a demonstration of raw power. Let your character see the truth, accept it, and then spend the rest of the book learning the intricate rules you've set up. And have some fun with it, because if you're not having fun, no one is.