Several different ways...
The main way for myself personally is
1. Just play over the games quickly without looking at too many variations with board at hand.
Was there a point when I went- what? Seems an obvious counter!? But, why can't I play that. Look it over myself and find the solution
Hopefully- sometimes it does take me a couple of hours collectively to find the actual solution. But, after that hard work you will HAVE to had learned something. If I get too frustrated with the position I will set it aside and come back to it later. If after coming back I still can't figure it out I will go to a computer for assistance.
This technique is especially helpful in reading opening books. Then your opening study also becomes tactical and strategical study.
2. After you have gone over the problems that you couldn't see now go deeply into the variations they give (Now there will not be those why's getting in the way of you actually learning the main points of the "discussion". It is sort of like scanning through a chapter in a textbook and highlighting all the words that you don't know and figuring out the definition before actually digging in.)
3. You can also practice playing blindfold games....But, I would suggest that you don't try to learn an opening this way. If you already can play blindfold then by all means do it- but, if like most people you can not see all the variations I would not suggest combining learning how to play blindfold and learning a new opening (or endgame or whatever). It would just be too much. So basically for most people just trying to go progressively over more moves. Maybe take an opening you already know very well. Try and go over the variations in your head. You can get out of the opening well now? Now find a miniature and try to play through the game in your head etc
I am sure there are other ways but these are the ones that pop into my head at the moment

Hi,
maybe you recognized at my account-name, that I speak in detail about Shogi (japanese chess), but in general about the whole chess-family and even much more (the game Go, othello, ...).
My question is for all kind of "such" games, like chess, xiangqi, go, ...
Many books are of the type "teaching with commented games".
(Okay, you can say, if I don't like such books, I should buy other books, but in shogi there is not such a big choice.)
This books often contains commented games with many moves (!!!) and less diagrams (!!!).
To better understand, for example look here:
http://eric.macshogi.com/shogi/handicap/handicap-4p-1.html
(It's shogi, but you can find similar for chess also very often.)
So my final question: how to learn best with such literature???
Finaly I will give a few answers to my own question:
1) Also reading in a comfortable arm-chair and make all thinkings completely in brain.
It's not possible for me to do it. For doing it, you must be able to play (almost) blind shogi/chess.
But on the other side, being able to play blind shogi/chess is also good for your playing strength.
So maybe it will be the best idea to practice playing without board (and make special training to be able to do so - what? how? ...)?
This would be very hard for me.
2) Or maybe better take a real board, sit at a table and make the moves there with your book beside?
Still I don't like this so much.
Also, I have seen (chess-) books, where are very, very long variants written (still complete games as variations!). In such games, it wouldn't be possible to even calculate the variations in my head and there will be the need to make the variation-moves on the board, too.
But then to come back to the beginning of the variation, you need maybe a second shogi/chess board, one for the main tree and the other for studying variations.
Not nice.
3) You can use computerprograms (for example Chessbase or BCMShogi ;-) ) for studying such games.
But still I even don't like this so much. :-(
I don't like to read books on the computer, I don't like to sit all my time on the computer (better reading on the balcon, in a nice meadow, ... ;-) ).
Furtheremore, such programs makes the live TOO easy!!! This mean, when I have a question and didn't understand something immediately, I can try (play) this variation and look at the help of the computer. Then of course I will say "oh, that's the correct move", but in this way the effect of remembering and reproducing such moves is not as good.
This is the same thing I spoke above: learning playing shogi/chess without board would be HARD work, but when you are able to play blind, it makes your play stronger!!!
But there is the questions: is it TOO hard, to learn it (for shogi)?
How do you learn with commented games which shows only a few (or even none) diagrams?
That's all my thinkings for the moment.
Thanks,
Bernhard