I basically agree with Cyriac, but have one added training twist. That is, I try to read accounts of games without the use of a board. That is a test of one's memory.
Of course, everyone knows how the board looks at the beginning. Say White moves 1. e4, Black e5. That's just a standard king's pawn opening. Say the next moves are 2. Nf3, Nc6. Now you know that you are heading for a Ruy Lopez, or maybe a Guoco Piano or Four Knights' Game. The next move seals it; 3. Bb5 a6. Now it is a Ruy Lopez. Play the game in your head, from the "score" without looking at a board.
One help in most chess books is that there is a diagram every 20 moves or so. Say you are fine up to move 12, and then get lost. Then look at the diagram. You can use it to "look ahead" to the 21st, 22nd, 23rd move, etc. But also, "retrace the moves. What did the board look like at the end of move 19 before the 20th moves were played? How about move 18? Go back to move 17, working back toward the picture you had at move 12. Try to "reconcile the two pictures.
You might work up to move 12, and backward from move 20 to move 15. Then you might need to play out moves 13-14 on a board. But use this only as a stopgap and train your memory and visualization skills.
One way to train yourself to play blind is to (initially) allow yourself a look at various intervals, say move 15, move 25, move 35, etc. Then lengthen the intervals so you can play a game blind.
I have deliberately NOT included diagrams to illustrate the thought process.