I'm not entirely sure how you would do it if you are playing through the itch.io app. Assuming you downloaded a standalone version, it depends on if you are applying a minor patch (going from version 0.56.0 to 0.56.4, for example). Or if you are updating a major version (0.55 to 0.56, for example). If it's a major version, install the new version of the game, and copy your save folder from the old version to the new version, then start the new version. If it's a minor patch, download and unzip the patch, then copy and paste over it's contents into the base version of the game, inside the "www" folder. If you did it correctly, it should ask you to overwrite some files with the same name.