The only way to learn to be an effective sight reader is to practice it.
Concentrate on reading above and below the staff notes.
I sometimes practice hand excericises with my eyes closed.
this familiarizes your fingers with the keyboard.
music.stackexchange.com/users/66004/Flashshockley
Learn to know the keyboard like driving your car: orientation on the keyboard: a) all 2 black keys open eyes b) with closed eyes) Find all 3 black keys (all octaves), in the same way: all 2 black keys, all EF and BC (the white semitones), all D (between the 2 black) all DC, triads and scales Play ceg, dfa (the scale of C)
blind, always stay in contact with the black keys and always mind the shape of the pattern.
Play the scale of
B major:1231234 (thumb on B and E) go through all sharp keys
the accompaniments of the l.h. are often triads and tetrads up and down.
Practice them in all keys, always analyzing the You can invent similar short orientation exercises and practice them without shhet music, blind, but always imagine or singing the notes you‘re playing, 2-3 minutes before you start reading.
Another way is reading and playing bar by bar or phrase by phrase, memorizing the keys and notes, seeing and blind, but always listening.
At the end you can play the piece by heart.
Btw.
it‘s not just a bad habit to look down on the keys
: you can also express a lot of music by looking down.
You have all the time of your life for reading notes, stay in contact with your piano, it loves, when you look into its (k)eys.
music.stackexchange.com/users/56219/Albrecht Hügli
http://www.micrologus.com/courses/sight_reading_method
For disclosure, I worked on developing the above system.
music.stackexchange.com/users/58618/MMazzon
There is a kind of hymnal (Reformation church) that uses only long note values for four part harmony.
Like The Scottish Hymnal .
I think these can be good for sight reading for a number of reasons: lots of (homophonic) music is based on adding rhythmic figures to a basic harmonic framework, the long note values in these hymnals focus on only those important harmonic tones most of the movements from chord to chord involves only single step motions or held tones which you can use as "anchors" for changing your hand position without looking at your hand
a lot of harmony examples are packed into a short space
most of the key signatures are easy If you practice playing double notes in one hand and changing fingers on repeated notes, along with sight reading the hymnals, it really help develop skills to play without looking at your hands.
At least it's helping me.
music.stackexchange.com/users/23919/Michael Curtis
My son worked with a sight reading book series by Paul Harris.
It was excellent.
I'm sure there are other good ones as well.
Each exercise is short, and includes phrasing and dynamics.
Interestingly enough, that is helpful.
In addition, the exercises are extremely graduated.
Also, the student is given a procedure to follow.
Look over the exercise carefully before putting your hands on the keyboard:
time signature, tempo, key signature.
Count out or imagine the rhythm once through, without playing yet.
Also, look at the melody and ask yourself, what scale degree is this starting on? -- this can help one visualize , so to speak, what the melody will sound like.
Some knowledge of music theory will be helpful.
The main thing is to work at your level -- which will be lower than the level of your repertoire pieces.
Imagine it as well as you can in your mental ear before you play it, and choose a very slow tempo -- and stick to it.
Give it phrasing.
Make it beautiful or at least interesting.
music.stackexchange.com/users/19678/aparente001
No short cuts.
Suffer like the rest of us!!
And no book recommendations either.
Know your scales thoroughly.
12 majors at least.
Harmonic minors would be next.
All without reference to the black and white keys.
Before starting any sight-reading of a piece, play through its key scale several times
- this gets your head and fingers in the zone of that key.
Concentrate on one hand at a time initially.
Remember there are two aspects involved in early sight reading - rhythm and melody.
Split them, starting with the rhythm part.
Tap out the rhythm of the notes, a few times so it's internalised.
Almost learned if you like.
You're learning to sight-read.
Only then try playing the tune, which will fit better over the rhythm you've established.
With no music, try to feel how far a stretch various intervals are.
M3,m7
, P5 etc.using different fingers in different keys.
Take some time trying out sight singing.
Keep to mainly white note keys initially.
Give yourself the occasional note as a check, and work through a single line melody slowly.
I've always said if you can sing it, you'll play it more easily.
A few ideas out of many.
Just practise sight-reading every day, and it'll get better.
Gradually or quickly - we don't know!
music.stackexchange.com/users/2808/Tim
Are there any recipes/shortcuts that can train a piano self-learner into being able to sight-play, at least simple pieces? How to overcome the difficulty of constantly checking the keyboard while reading notes?
recipes of piano sight-play for a self-learner
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<piano><sight-reading>
music.stackexchange.com/questions/94708
music.stackexchange.com/users/66003/feynman
Learn to orientate yourself on the keyboard blindfolded using orientation exercises without sheet music but while singing  the notes you are playing. Another way is to read the sheet music and playing it bar by bar and memorizing the keys and notes.  Learn to know  the keyboard like driving your car. 
Learn to know  the keyboard like driving your car. Find all 3 black keys (all octaves), in the same way. All EF and BC (the white semitones), all D (between the 2 black) all DC,   triads and scales. Another way is reading and playing bar by bar or phrase by phrase; memorizing the keys and notes, seeing and blind, but always listening. At the end you can play the piece by heart.