How do professional chess players think ?

Possibly of interest:
100 Chess Master Trade Secrets by Andrew Soltis
https://web.archive.org/web/20140708094523/http://www.chesscafe.com/text/review916.pdf
Reaching the Top?! by Peter Kurzdorfer
"... On the one hand, your play needs to be purposeful much of the time; the ability to navigate through many different types of positions needs to be yours; your ability to calculate variations and find candidate moves needs to be present in at least an embryonic stage. On the other hand, it will be heart-warming and perhaps inspiring to realize that you do not need to give up blunders or misconceptions or a poor memory or sloppy calculating habits; that you do not need to know all the latest opening variations, or even know what they are called. You do not have to memorize hundreds of endgame positions or instantly recognize the proper procedure in a variety of pawn structures.
[To play at a master level consistently] is not an easy task, to be sure ..., but it is a possible one. ..." - NM Peter Kurzdorfer (2015)
http://www.thechessmind.net/blog/2015/11/16/book-notice-kurzdorfers-reaching-the-top.html
http://www.jeremysilman.com/shop/pc/Reaching-the-Top-77p3905.htm
Think Like a Grandmaster by Kotov
Train Like a Grandmaster by Kotov
Becoming a Grandmaster by Keene
What It Takes to Become a Grandmaster by GM Andrew Soltis

As far as I've observed, Masters think squares, Patzers think pieces, LOL.

It is a common myth between many people, be it a chess player or not, that chess masters can calculate chess positions as far as 25-30 moves ahead of current game scenes.

Great chess players do think ahead but not that far. This is probably because they have to think laterally too. This creates a possibility for many scenarios coming into play.

During the endgame is usually the common time for most chess masters to think several moves ahead. There are chess masters like Magnus Carlsen who claim they can see up to 15 moves ahead and at times even 20.

Thinking many moves ahead may limit you to just calculating along one line. You are supposed to put into consideration several lines your opponent may move along and calculate the moves in each line.

most of the thinking happens in under a minute via intuitive pruning. the rest of the time is testing out candidate moves and the odd novel idea that may pop into mind that is  not within intuition range (calculation of candidate moves often reveals more possible ideas, if not if all candidate moves reveal something ugly , you start searching for creative solutions).

ever seen how easy a 2000 dispatches a 1500? yes part of it is more general knowledge, part of it is faster (or at least more efficient )calculation, prob the endgame is much better, but by far the most telling difference in their strength is the intuitive matrix of moves to prune. expert has a decent understanding of the flow of his pieces and that shapes his conceptual landscape of candidate moves, the 1500 has mastered basics and is consciously trying not to blunder half the time. This is how a 2000 playing with his food can easily overwhelm an ok class player with minimal effort. One's basic intuitions is another's novel revelation.

This book and 2 others by Soltis -- The Inner Game of Chess and How to Choose a Chess Move -- give great insights into how chess masters think.

Pro players aren't just trying to find the strongest moves on the board ... they're also considering their current standings in whatever tournament they're playing in ... as their standings affect how they should play (safe, if ahead; aggressive, if behind ...).

They're also thinking about the tendencies of their opponent, based on the previous games of theirs that they've studied ... as well as the current standings of their opponent, too (because that, also, will affect the way the opponent is playing).

So for pro players, it's more than just looking at the board and playing the position ... it's also about playing the field around you, and choosing moves that, psychologically, will undesirable for your opponent, based on their current tournament needs ...

It's a deeper game than just the board alone.

From what I've read, GMs spend a lot of their thinking time on figuring out what their opponent is planning and how to prevent it. (I certainly dont!) The result seems to be that winning by executing long term plans seldom happens in GM games.

I watch a lot of Jerry (ChessNetwork on YouTube), where he plays games here or on lichess and explains his thinking as he goes. As @SwimmerBill says, a lot of his thinking is about preventing his opponents from getting their way. A lot of it is also about the relative strength of the minor pieces. He is able to calculate variations much faster and more accurately then I can - I have to keep pausing the video to keep up.

I suspect a lot of it subconscious pattern recognition though, and difficult for him to explain because he's barely aware of it.

I'd strongly recommend ChessNetwork videos on YouTube to anyone who is unaware of them. Not only are they instructional, they are also highly entertaining and he has the most soothing voice I've ever heard.