Mastering the Chess Openings (Volume 1)

Based on your rating, I think you would find Mastering the Chess Openings to be way, way too advanced. You should start with a book that covers basic opening principles, not detailed analysis of theoretical lines, and then do a ton of tactics exercises.
To more directly answer your question, I usually play through the moves in books using a board on a computer. It's much easier to set up positions. I try to calculate all variations in my head rather than moving the pieces in order to improve my visualization skills. If I just can't follow a variation in my head after several tries, I will play out the moves of the variation on the board.