This is how I proceed as a Windows user:
- Download the game
- Extract the content to a new folder, not the old game folder
- Inside the old game's folder, go to the directory \game\saves\
- Copy all files with the extension .save to the same folder in the new game location (create it if it is not there). Do not copy the file "persistent" as you will probably not be able to start the game if you do.
- Start the new version of Holiday Island and check whether the transferred saves are found.
If you cannot find the old saves in said location, you can check if they are in the following folder:
c:\Users\<your user name>\AppData\Roaming\RenPy\Island-<some number>\
When I am certain that everything works as expected, I delete the old version of the game.
In any case, I keep a zip of the old save files on an external hard drive. So if anything goes wrong, you can still recover your game later.