I'm always experiencing difficulties while trying to visualize what moves a tutorial (or an answer here for that matter) is talking about unless I have a chessboard with coordinates nearby.
Is this something I should fix, or is it fine to be using a chessboard? and what can you advise someone who want to memorize it?
The easiest way to visualize the board is to practice! I know that sounds trite, but there aren't really all that many shortcuts. Go over games in magazines. Start from one of the positions given as an image and then "make" as many moves as you can in your head. Try to see the position and look for the threats and ideas of each move. If you can only make one move, that's fine - it's a good start.
Similarly, you can use a physical board when you're going over a game. Play out the moves on the board and start to learn the squares by name as opposed to figuring out which square is which each time. That's probably the first step. After you know the "names" of the squares, the rest will start to fall into place.
There are books available that promise to directly improve your visualisation skills (like "Chess Visualization Course" by Ian Anderson, which I haven't read myself).
But the easiest way to improve your visualization skill that might even make you a better player in more regards is: Reading tactics books (like "1001 Winning Chess Sacrifices and Combinations" by Fred Reinfeld). Trying to find the solution without the help of the board is a great way to learn thinking ahead. A great introductionary book to start with (beginning with 1-move-mates) is "Chess: 5334 Problems, Combinations, and Games" by Laszlo Polgar). This way you have tons of material to practice your visualization and hone your tactical prowess at the same time!
On Chess.com you can use the mobile app, then click the three bars (menu) and then click 'vision'; this is basically a game where you look at blank board and it says 'g8' then you hit g8 with your thumb then it goes 'c3'etc etc. You are doing this against time you get a score and all at the end of the time but it does help memorizing the spaces, I've found. After you know the board the pieces algebra comes easier.
Rather than relying on any one suggestion you might want to do a bit of them all. A good start is being able, after you are given the name of a square, to say without hesitation what color it is. To make things more precise, it helps to recall, for example, that b5 is the square that the Lopez bishop goes to. What other squares are important in your favorite openings?
I'm an Android user so I can only speak of Androids but there are chess memorization mobile apps. https://play.google.com/store/search?q=chess%20board%20memorization&c=apps&hl=en
I would guess that there are apps for Apple as well that are similar if you are a Apple user. I just don't have a way to give you search results since I'm not a Mac user.
http://chesseye.alexander-fleischer.de/ has a training tool just for this purpose.
Of course practicing helps, just like in any sport, but there are also TECHNIQUES that make any skill easier to do correctly or to improve more quickly.
At each move or whenever the board is not completely clear, say these words:
"Fix the board in my mind: King is there/F8, my Queen is there/H7, that/G8 is empty, that/D3 is empty".
Don't let naming the squares get in the way of visualization -- both are useful, but practice naming and finding the squares separately -- especially if naming them isn't completely easy or interferes with SEEING in your mind.
It's fine to name them if you can do so fluidly, otherwise merely say "there" and "that" or "next to Pawn"
Generally avoid mentioning pieces that are gone; captured pieces are covered by EMPTY and saying where active pieces are NOW located.
Do include "EMPTY" in your list, both to see open lines and to firmly fix where pieces can now move, as well as to stop "interference" from the real/computer board with the one in your mind.
This is NOT as good as eventually being able to "just do it" but it's a technique anyone can do IMMEDIATELY, even a beginner, to improve right now and work towards better visualization through automatic methods.
With this method, you can continue to look at the actual (or computer) board and just update empty squares and pieces standing on new squares of the BOARD IN YOUR MIND.
At any stage or whenever needed, repeat the process to update the board in your mind -- just doing the process will increase your future ability to visualize, along with clarifying the current board.
A beginner may need to do this after each full move, or even after each half-move at first, while someone with a bit more skill may do it only every 2, 3, or more moves.
Just repeat it as necessary, or use it whenever vision isn't as clear as you wish it to be.
