How do pianists improve their sight-reading skills? They work at it. In fact, at Listening House, we actively teach and drill some important concepts.
For several weeks each year, my students complete sight-reading assignments. I lend them books that are a level or two below what they normally play, which is standard procedure for sight-reading. Then I ask them to follow these steps with the new music:
1) Look it over carefully. Notice the form/pattern of the composition. Look for repeating patterns in both the right and left hand. Are there sharps or flats, or odd fingerings, or anything else you need to know?
2) Count aloud as you tap the rhythm with both hands.
3) Set the metronome on a low speed and play straight through the piece, just once, with no stops.
4) Analyze problem areas. Where did you make mistakes? How can you correct them next time?
5) Re-set the metronome and play straight through the piece again.
Following these steps, even for a few minutes a day, can dramatically improve sight-reading.