Set out a chessboard. Be sure to use a set that has algebraic notation on it: Algebraic notation is a way for you to read the moves and then play them on the board for each side so you can follow a game and study what each side has played, and analyze the moves. Across the bottom will be the letters from "a" to "h." the letters will not be capitalized. There will be numbers going up the sides from "1" to "8." Each square has an address. The first square on the board is "a1." To represent a move, start with the first letter of the piece, capitalized, then write the square you moved it to. If two different pieces that start with the same letter can move to the same square, then include the square the piece originated from. Each piece starts with the first letter of its name, except for the knight, which starts with a capital "N." If it is a pawn, then just write the name of the square it moves to with no capital letter. Castling is written 0-0 for king side castling and 0-0-0 for queen side. There is more to explain about how to notate a chess game, but for now, just follow the directions to get to a certain position where the visual exercise will begin.
Play the following moves, moving for each side. 1.e4 is a white move. 1.e5 is a black move. In a score sheet it looks like this: 1. e4 e5. Next play 2.Bc4 Qf6. Next 3.Nf3 Qg6. 4. Nc3 Qxg2. When there is a small letter x, it means capture. So the Queen has captured the pawn on g2.
Begin the exercise. Though you will be calculating white one's move, you will be visualizing for both sides.
Analyze what has happened first. The queen has taken a pawn. It's not good to lose pieces or pawns willy-nilly (giving pieces for free is called "hanging a piece", but it's also not generally a good idea to move the same piece twice in the opening, nor to move the queen out first, as she is such a powerful piece that she becomes a target and can get trapped. Greed can also get you into trouble, especially if you go attacking before your pieces are developed. Also there is a saying, "Loose pieces fall off, meaning that pieces that are not protected can become targets of fancy tactics. So knowing these things, let's see if you can find a way to punish black.
Calculate. Find multiple candidate moves. Go down the branch of just one of them. This is what it means to calculate three moves ahead. You don't just pick one move and follow it. You pick as many as you can, and then analyze each one, finding the best possible moves for your opponent as you can, and seeing if you have a good response to it. There is a rule among strong chess players that says "Look at all checks and captures." There is a move here that satisfies both. Look for a moment at the board and see if you can figure out what it is, and then go on to the next step. But first look for it.
Start to visualize. Did you you find Bxf7? That's the one. So now comes the visualization part. Don't touch the pieces - do this in your mind. Visualize what the board is going to look like after you play Bxf7. See the piece there. While visualizing the piece there, ask "what are all of black one's options for getting out of check?". How many are there? That's right, there are three: The king can capture the bishop on f7, or he can move to where the queen used to be, on d8, or he can move forward one square to e7. Visualize the king capturing the piece on f7. See in your mind the new position after these two moves have been made. Hold the image in your mind as clearly as you can. Next ask what white can do from here. What moves can white make in this new position where black one's king is on the f7 square? Name several possible moves, and look for one that checks because you always want to look at all checks and captures first. See anything good? You could check by Ng5 but there is a problem with that. The queen is guarding that square and will capture. So how can you move the queen away. How about put the rook on the g-file? Visualize the Rook moving to g1. Now where can the queen go? Only one square. Visualize the queen moving to h3. Now you can check with the knight. Notice anything else about Ng5? That's right, it's a fork. You win the queen. So you sacrificed the bishop to win the queen. Not bad. Do you see any better moves for the black queen? No. Probably just to take the rook on g1 to get as much as he can out of it. Can you reverse the order of these moves so he can't do that? How about instead of Bxf7 first you do that second, after chasing the queen to h3. Now you can get the queen with a minimum of losses. Of course, you also may have tipped off your opponent to your plans by chasing his queen to the forking square.
Keep practicing. After trying this exercise, you will have visualized three moves ahead for one move. In a real game, aim to analyze more than one move. Go through this process for each of the moves that you are considering. The further you are able to go, and the more vividly and accurately you are able to visualize the positions two or three, or even four moves ahead, the better chess player you will become.
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