Contributing to this long and exhaustive thread for 2 reasons:
a) adding another voice of encouragement to those starting out on this journey. I went from being an abysmal reader, painfully deciphering note by note, to being reasonably fluent. How? Simply by doing it, every day.
b) I did do one thing slightly differently from the standard advice. I play my sight-reading pieces more than once, and go back to them for 2-3 days. My reasoning behind this is that I want to acquire a "passive knowledge" of shapes and patterns, much as a language learner would. For example, French (and Italian, Spanish etc) children instinctively learn how to use the subjunctive years before they are able to understand how and why there are doing so: they learn "by ear". I'm trying to do the same with music. I've also developed this passive database by doing the 40 pieces a year challenge: making a point of learning many, varied pieces.
I couldn't quantify how long this has taken - years rather than days. And it's work in progress. But after a couple of years the difference was already staggering.
So anybody thinking of trying, do!