When reading books like Sorcerer's Apprentice or Life & 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.
Should I set up the position on a board or on my PC or just try to imagine it in my mind?
Yes, depending on what you have available, this is the best option. Imagining it in your mind ('blindfold chess') will help with your calculation skills; in a real game of chess, you do see a board but you are not allowed to move the pieces to analyse the position.
Using a real board for playing along with the book is easier and recommended for non-advanced players. A chess program will have the benefit that it can tell you other moves to look for, or if you want to analyze a sideline which is not covered in the book.
After reading through the moves I often feel like I haven't gained any knowledge.
Exactly. It's then just like reading a dictionary; you understand the words but you'll never learn them.
What I always used to do (this was back before the PC was invented, when dinosaurs walked the earth) was set up my magnetic travel set with the position of the game, and make the actual game moves on it, then set up a regular chessboard on the table and play through all the analysis of the game on it.
That way I always had a reference of what the game position was, so it was never lost and I could return to it easily if my analysis went too far afield. And that also meant I could use the "analysis set" to chase down any other variations that I was curious about that the author didn't mention, as well as follow the author's analysis better.
