How to learn from published game collections

I have a couple books containing chess games and analyses--The Most Instructive Games of Chess Ever Played by Irving Chernev and Understanding Chess Move by Move by John Nunn. What is the best way to learn from these books? I can play through the games, either with a chess board or on the computer, and try out the alternative lines to see why they might be better or worse; what else can I do to study these games, so that my own playing will improve?

I also would like to hear a response to this question.  Logical Chess:  Move by Move....should it be gone through several times?  Once straight through, but then with detailed study and notes?

I would also like to ask if many can read and follow the games without a chess board set up, and if so, about what level does this become a comfortable acquired trait?

Thank you!