Can't say for the android version, but for the PC you just download an archive and unpack it. There is no launcher in the game that checks for updates. You just run the game by exe file from the game folder. To update to the new version, you download the new archive and unpack it as well. In theory, you can do it in the same folder with replacement of old files, but it's better to do it in a new folder. The old version can be safely deleted. The saves are stored in another folder (for windows it is in appdata folder)