I have been asked to be more precise about what I am doing. Well, let's have a try. First I give some definitions of what I am speaking about. Second, some variations of exercises. While MDLM suggested to use an empty or nearly empty board, I prefer real chess positions or whole games for my board vision exercises.
X-Ray: Look at the squares that are under control of a piece regardless of the possibility that the piece can reach these squares or not. This means looking through the pawns and pieces that are on the board, in the manner of an X-ray device. In a strict sense only long-distance pieces such as Q, R and B can do X-Rays.
Real Scan: Look at a real piece on the board and have pop out all squares under control of that piece.
Virtual Scan: Look at any square on the board, regardless of what is on the square, assume that a certain piece is on that square and do a scan for that piece. A variation of virtual scan is the Chameleon Scan, that is doing a K, Q, R, B and N scan from that square. The sequence of these scans may vary.
Pawn Scans: If pawns are connected, then have pop out all squares under control of the pawn chain at once. With pawns I only do real scans, but maybe virtual pawn scans would also be a good advice. I never tried.
OTB Exercises: Use a real chessboard and pieces of wood, and real games. After every move (ply or full move), do a lot of (virtual) scans, preferably from every square of the board, beginning for example with a8 --> h8 and ending with h1 --> a1. You also may use the spiral pathway MDLM describes in his concentric cercle exercises. Going through a game changes the position all the time, and this is important, because the real position on the board interferes with the scans, making them more difficult than just on an empty board.
Screen exercises: Go through real games, after every move do a scan from the piece or pawn that has moved, then go to the next move. The goal is to use less than one second per ply without much effort. I call this exercise X-Ray Jogging. While jogging through a game this way, try to get as much as possible from the game: What threats emerge, how can they be parried, what is the general strategy, who stands better, and the like.
Advanced exercises: I am far from these, still working on the simple ones. But if a simple scan can be done in, let's say, 500 or less milliseconds, then the next step will be to do scans not from single pieces to squares, but from multiple pieces and pawns to board regions (for example, whole mate nets popping out immediately).
Board Vision Days 10-12
4 hours of X-Ray Jogging, speed: 2.3 sec/ply (goal: 0.5 sec/ply)