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How do you memorize the coordinates?

The same technique I used for simple math. Memorization by rote.
#1...Lichess has a coordinate training program. Click on "Learn" select "Coordinates" You can also start hand recording your game record, as you play. That's a really great way to learn it. I used that technique to learn descriptive notation back in the day. :] #5 I assume that you didn't even read my post...I thought there was an echo in here.
Practice your coordinates on lichess.

Watch chess games and listen to commentary.

Play lots of games from both sides and notate them by hand. This will give you a feel for the squares. Most squares are occupied at some point or another so you'll get used to their position and what they mean during a chess game.
You can try and memorize them but it seems inefficient to me.

Squares have meaning. For example, I know e4 is light because I play 1.e4 and put a pawn there on my first move in half my games. I also know f7 is light because it's a focal point of a lot of attacks especially by the light square bishop. I know c5 is dark because its the first move of the sicilian and also because black can establish dark square control in a variety of openings with c5.

You can also sit and close your eyes and try to visualize the board. See all of the various lines and diagonals and then ask yourself where various squares are and try to see them in your head. You can do the same thing when reading a book. Play the lines out in your head as much as you can. It will vastly improve your ability to calculate and also help you learn blindfold.
Take a board and pieces made out of wood and put it on a table. Play trough some games out of a book etc and then you got it.
I agree with #5.
When I started out I wasn't really good getting used to the coordinates, but it was and really is the only option to learn how to communicate moves, so I was forced to learn it.

Play games and watch commentary videos as #5 said, and within a month or two you should be really used to the coordinates

Eventually you want to be able to say the moves and squares without any thinking at all, and know what squares are next to/lined up with other squares, so you can essentially talk about chess in your sleep or at lunch and discuss moves without looking at a board, stuff like "then he pushed his pawn to d5 kicking my knight on c6, but that opened up my g7 bishop" and you should be able to picture it
Hi @LudwigChess, cool question. It is similar to when you are learning the alphabet or numbers when you are in school. It begins a total mystery, but with repetition and familiarity, it becomes easy and natural. It is somewhat similar in size too; 26 letters in the alphabet and 64 squares on the chessboard, which should be very encouraging -- you can do it! It is also very similar to learning the piano and being able to know what note goes with which key (middle C, compared to just a bunch of random keys). The more you know what you're looking at, the better you can play it.

Begin by familiarizing yourself with the concept of "algrebraic notation", if you haven't already, so you know the idea behind it.

Next, review your games afterwards, to see the list of moves. They are probably confusing to see right now, but it gets you used to seeing them. For example, you will see that every time you move the king's pawn 2 squares, it'll say e4; when you move black's kingside knight to its most natural square, it'll say Nf6. These might be utterly insane and alien concepts right now, but through repetition, you will definitely get used to it as most of us have. You'll notice anytime that move is made, it's always called the same thing. Eventually you will have seen that same moved called the same thing so many times that it will be obvious.

Then, browse through the opening explorer / analysis board, which can help bring life and personality to those mysterious squares, like they are players on a sports team. You'll begin to realize that it's quite simpler than it originally appears. For me, I started to "get it" when I realized just how few squares the pieces can actually move to, especially in the opening. For instance, white's dark-squared bishop is generally going to e3 or g5 in the Sicilian. Or, black's queenside knight will go to only c6, d7, or a6. Realizations like these reveal the chess alphabet to be very finite, rather than infinite.

Just as when learning a regular language, first we learn the alphabet. Then we can build words, from words we can build sentences, from sentences we can build paragraphs and so on. Once you are comfortable with individual squares, there is no end to how much farther you can go. As #8 suggests, you'll be able to trivially know things like Nf3 and Bg7 both attack d4 before the match even begins. At a certain point, I recommend making a list of all of the diagonals in particular, and what squares are on each of them.

Related humblebrag side note -- I won against a chess friend while only I was blindfolded (irl) and he has refused to play me ever again in the year since :)

My final tip and exercise -- everytime you see a chess position: consciously identify what square each piece is on, for both sides. Eventually, those squares will transform from being meaningless to meaningful -- alive with distinct personalities like on a sports roster.

When I was a kid, I just took a book with some games and played them out on the board (I didn't have a computer back then). After like a dozen games, maybe a bit more, you remember everything. I never even understood why remembering coordinates is an issue.

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