How should I read chess books that show games or parts of games? When reading books like Sorcerer's Apprentice or Life &amp; Games of Mikhail Tal, often a position is shown followed by a list of moves, then another key position, then more moves, and another position, and some reasoning.

How should I read this part?

Should I set up the position on a board or on my PC or just try to imagine it in my mind? After reading through the moves I often feel like I haven't gained any knowledge.
It depends on what you want to get out of the book.

If you're reading for enjoyment, read the text, try to see the point behind the nice sacrifices, and relax.

But for study, you need to do something else: set up the position on a board, put the book away, then try to understand the position on your own. What are important features of the position? What is each side trying to achieve? Are there any tactics or threats? What's the best move?

Then play through the moves in the book. Try to understand them, how do they related to what you thought each side was trying to achieve? What was it you missed? Why are these moves best?

Basically, for study, treat every diagram you ever see as an exercise. The improvement in your chess skill will be directly proportional to the amount of work you put in.

Of course one doesn't always feel like doing that, and that is fine too (I love just browsing chess books). Just don't expect much real improvement then.