The more you use a board, the more you'll remember. You might even cover the moves, analyze the board and try to guess them before you read them.
Analyzing books

Yes i think it would be vital to have the BOOK in front of you lol.
You should try to do it in your head and then if you have trouble following the position do it over a board or computer program. However, I would think playing over the board the would help to enforce the ideas better. use the computer or second board for varations.

I generally work through famous instructional games (the Irving Chernev book) by playing on the side of the eventual winner. I go through move by move and often repeat motions in the opening so that I can get used to the openings and variations.

When reading a book, should you have a chess book in front of you analyzing every move on the board, or should you concentrate on reading the book in your heaed?