Here are some thoughts from a seasoned sight-reader.
The most important thing about sight-reading is not to see how many notes you get right, it's to see how quickly you can understand what the music is about.
Think of learning to read a language. You first learn to understand and speak your language. Before you start learning to read, you are already fluent in speaking: you can take part in conversation, listen to stories, tell stories, recite poems... When you begin learning to read, at first you're stumbling over individual letters. You get used to combinations of these letters making up words which you already know. Then you string these words together and get to the stage where you can read a whole sentence and grasp what it means. When you've got this far, you start reading stories, and if you take delight in discovering new stories, you read more and more and become a fluent reader.
For me, it's logical to learn music the same way. You start by listening and copying, you get familiar with the sounds, you learn to play simple tunes, you get the feel of certain chords and rhythms, and only then do you start learning how all this is communicated through dots on a page.
I think many adults get the idea that they should be better at reading and look for recipes to learn to sight-read fast. They need to understand that learning to sight-read takes time and goes hand in hand with learning about how music works: harmony, rhythm, structure, style... The nice thing is this: once you get to the stage where you can read music - not sight-reading at super speed, just the basics - the more you read, the more information about music theory you will assimilate without having to consciously analyse it. It's just like reading books in your language: the more you read, the more you gain an "instinctive" understanding of grammar and style, how to tell a story well, or how to tell one badly.
So for beginners:
Don't get in a sweat about sight-reading, give it time!
Just remember read music that is new to you from time to time. Slowly, not too much at once. Think of it as reading a story: you want to enjoy it, not push through relentlessly even if you're not understanding what you're reading. When you listen to a recording, see how well you can follow with the score.
And for more advanced pianists:
Read through lots of music for the pleasure of discovering it!
Take a piece you don't know and read it. Don't try to play it at speed, don't worry about stopping or going back over something, but try to get a feeling for how it should sound. What's the key? What's the mood? Do you understand the harmonies? If you come across some tricky rhythms, see if you can speak or tap them. If a passage sounds weird, play it again to see if you got the harmonies right. If a passage sounds particularly nice, play it again for the pleasure! When you feel you have a good idea of how the piece should go, you could listen to a recording and see if it comes close to your imagined version.
The more time you spend discovering music like this, the nearer you will get to what might be called "real" sight-reading: keeping time and not stopping while managing to get enough of the notes, rhythms and dynamics right so that you manage to convey the essence of the piece.
). If you can get those books then definitely do so.