The process is different from game to game. In a lot of projects you can find a directory called “saves” or something similar, and usually you can copy that to the directory of the updated project.
However that might not be as easy for some games. In some cases, from inside the game you might be able to “export” the save data to a file, and “import” them from the new version of the game.
If still unsure, you can contact the developer on how to do that, they would know for sure how this is done.
Hope that helps :)