1) Exposition in story: Have some incidence take place during a class in high school where the teacher incidentally explains it all. Have the character muse on the progress of science. Have characters converse about the nature of magic.
2) Exposition by narrator: The impersonal voice that usually tell you what the characters are doing, also takes it upon itself to explain what's going on.
3) Footnotes or similar "out of character" texts, separate from the text of the story.
4) Appendix where curious readers can look up to see if they find anything about the thing they don't understand.
5) No exposition. If the use of an item or spell is not obvious, make it. As for why things are the way they are, who cares? It's not like common people ask that about this world, after all.
I'd be grateful if anyone took the time to comment on any of the above.