Improvement to your sight reading is done in two different ways, accuracy of reading and speed. Each one needs to be targeted seperately.
To improve speed of sight reading take these factors into account when sight reading;
1) Take out easy music, easier is realative to your skill. If Liszt Transcendentale Etudes are easy for you fantastic! But for all us lesser mortals some simpler pieces with repetitive patterns might be good.
2) Play at tempo or around about the standard pace, not slower.
3) Don't stop if you make a mistake. Your playing should sound horrible, but the idea is to keep the brain moving and eyes reading. This may be tough, we are often by habit want to correct ourselves, but we are not working the accuracy. The speed which is developed through putting ourselves in constant reading mode, even with errors in our fingers and notes struck. So long you keep moving through the piece and play the first note starting each bar correct (so that you generate a confident beat) You may feel completely lost but that is ok. Keep a few pieces to repeat this process for a few weeks every day and unavoidably you will increase the accuracy of reading too but more importantly your speed.
4) Neglect rhythm. This is developed mainly by your internal ear, not the fingers and does not have any place in accuracy or sped of musical reading. Play all notes the same, parts where movement of notes are easier you can speed up, harder sections may be slowed down a little. The music you sight should sound nothing rhythmically to what it sounds like when played well.
5) DO NOT watch your hands. This has no place in sight reading. Unless you can look at your hands and the page at the same time, but for us without individual moving eyes, do not sight reading and look at your hands. This is very tough at first because we feel blind to what we are doing. I will discuss how to develop a touch for the keyboard later. But for now use the 2 and 3 black grouped notes as a guide and feeling for the notes in between these and the 2 coupled white notes. These are what generate the basic feel for piano. Ask a blind man how he plays the piano and you will get great insight, looking at the hands disrupts the position of the eyes in the sheet music. It will slow the speed down and increase inaccuracy. Sighting now and again the hands mayy be important for certain movements of the hand however, but should be limited as much as possible even in large leaps.
6) Take groups of notes in one go, try not to read single notes, try to see 2 notes at the same time or even 4 or more.
Observe how these groups affect the hand and notice any repetition which comes up try to memorise what you did before. This will increase the speed of reading and develop your musical thinking, visualisation process and ultimately memory speed.
Increasing accuracy is very similar to improving your speed of reading but a few changes:
1) Super slow playing. Play at a pathetically slow speed, giving yourself enough time to read notes.
2) Play with 100% note accuracy. No mistakes are allowed here. Also this demands that you not look at your hands, but this rule is no as strict as speed. You should look if you feel you will play the wrong note. But if you look notice where the note(s) you should find by touch are. How ddi you get to it? How does that feel? What does that change look like on the sheet music? These questions have plenty of time to process with your super slow tempo.
3) Neglect Rhythm
4)Read in groups
5) Correct mistakes, which is logical since we are working on accuracy.
6) Try to find a super slow tempo that is constant and not changing in speed as we did in the speed training. Even if there are parts you can play fast with sight do not play them faster. Leave that for your speed training.
I would say 10 minutes sessions for speed/accuracy of reading is sufficient.You should strick to this for 2 weeks straight and then assess yourself. Neglecting one session here or there doesn't have the same impact of improvement but its of course better than totally neglecting this study in your daily piano habits.
One of the most important skill to have while sight reading is the ability to play without looking at our hands. Every time we look at our hands we take our eyes away from the sheet music, this in turn slows down our rate of reading and anticipation of what lies ahead. Why can a blind person play the piano without ever looking at the keyboard? There can be many reason, most people will say that they do see the keyboard but in a different way, so too we have to remove ourselves from only looking with our eyes and look with our mind and fingers instead.
Two Blacks: On the left side we have C#Db on the right side we have D#Eb
Three Blacks: On the left side F#Gb, the middle G#Ab and the right side A#Bb
This is fairly obvious to observe with our eyes, now you have to do the same with just the hands. How can you sense that there are 2 blacks or 3 blacks near our hand? How can we feel them beneath our fingers without having to play them?
The next pattern which is a little harder to see but still quite obvious are the adjacent white notes (that is white notes which are directly next to each other without a black note seperating them;
Two Whites: On the right base of the three black groups BCb and on the left base of the two black groups we have CB#.
Two Whites: On the right base of the two black groups EFb and on the left base of the three black groups we have FE#
(Note the two whites can also be considered as bases of the two blacks or three blacks)
Finally we are left with white notes which are between the black notes, that is the D between the two blacks, and the G, on the left side and A on the right side between the three black notes.
How does this help? We should refer each note we play with respect to the patterns described above. It might seem very long winded to see the piano like this, and it is when you first do it, but eventually it becomes quite habitual and subconscious and even while sight reading music we will start to think in our minds eye where the notes are, where our hand is at the keyboard without ever looking down. We have to make that effort not to look at our hands though, so thinking about these shapes and where notes are when we are playing is very important. A good excerises would be to play single notes, closing your eyes, and move up one octave and down with random notes, scale patterns. Move onto chords, feel the shapes, and where other notes you need to get to are before having to play them.
It is important when you correct your fingers after a mistake that you don't simply move the wrong finger into the correct postion and carry on. Correct the wrong notes, then reset the hand to play the whole group again, to feel what it should feel like when played right. Note errors do not help us to achieve muscular memory, they also do not help us to play without looking at the keyboard! So when you make these errors while sight reading make sure you start again and consciously focus your effort to hit the right note by observing the pattern in the piano, then forgetting about it once you achieve several successful repetitions.
To play without looking at hands requires that you play consistently correct to start off with. Making mistakes will cause more mistakes, and if the mistakes are random then you really have to work out the whys behind it before you can imagine to memorise a piece or even play it well.