Guide to using a book I am currently twenty years old. I learned the rules of chess when I was eight and played on and off for a long time. However, I did not take it seriously. Recently after joining chess.com and trying out the tactics, as well as following grandmaster games and YouTube channels, I am interested in improving my skills. 

As of now I am able to figure out tactics as well as calculate decently in situations where a few different permutations of exchanges or forks, 2 or 3 moves ahead, could take place. However, most text I see talk about pattern recognition and studying positions and tactics. Therefore I have obtained a copy of Susan Polgar's "Chess Tactics For Champions". I would like to know how I should go about using this book. I understand that it is quite comprehensive. But somethings I would like to get right the first time around are:

1) Should I make a conscious effort to remember positions presented in the book?

2) Should I make a conscious effort to identify patterns or relate positions other than the obvious differences? Or will I start to hone this skill automatically?

3) Should I try to set up a board and play on a few moves in cases where the objective is to get an advantage?

4) Should I keep in mind any trade-off between tactical advantages which may lead to immediate piece advantage versus positional advantage?
How you should use the book is really a matter of opinion, but I very much believe in immersion learning, so rather than do a few every day for a longer period, I believe that doing as many as you can in a shorter period of time is more beneficial. I have seen this play out in practice in both my progress, and in the progress of those, whom I have taught.

Therefore, I always say, that try and do at least 50 per day, spending no more than two minutes per move on each problem.

The whole point of pattern recognition is that you do not have to try to remember the specific positions you see in the book as you will likely never get those exact positions in your lifetime. What you will get in your games is certain elements of those games, the patterns", and by doing enough of these tactics exercises, you will start to remember them.

I just looked at the table of contents of the Polgar book, and it is well-organized. You want to stay within a certain type of tactic when you are studying, like doing pins for a while, and maybe later, forks, etc.

You should, and shouldn't, have to consciously identify the patterns. I think it will come naturally as you read that book, and MANY more tactics books after. Even if you become an "ordinary" Master, even then, your tactics will still always be helped by continued tactical practice.

I am not sure how number three relates, or really what you are asking, but in general, when doing tactics problems, I would not set up a board as it takes too long, and you want to start calculating in your head anyway.

A tactic can lead to either a material advantage, which I think is more common, or a positional advantage. You always need to be mindful of the evaluation at the end of a tactic, and ask if you are really better, and is there any trap at the end that you may have missed. If you have a tactic that can lead to either type of advantage, you have to weigh the pros and cons of each final position. I would say that, in general, material is more likely to be preferred, but there are definitely cases where I would not want the material, and would take the position.

For example, I recently answered a question here where the OP took the exchange. I would not have played the move 35...Ne3+ winning an exchange, and would have preferred to maintain the pressure. The short "tactical exchange" winning the exchange allowed white to use e4 as a blockading square for quite a while, whereas keeping the attacker would have probably led to more. The positional pressure was worth more, in my opinion. So this is an example of having a choice between material and position, and having to make a decision.