How do you make unsalted olives?
Short answer: Oven-dried olives are your only non-salted option.

Long answer:

Almost all olive cures involve some quantity of salt. Some olives are just brined; olives cured with lye are also brined; so-called "oil-cured olives" are actually heavily salted.  

Your only non-salted option are "oven-dried olives", a Tuscan specialty ... but they won't taste like the olives you're used to.  You might try them anyway.  I'll warn you though -- they're better if you add a little salt.