1. Download a file manager and access:
SD:/Android/data/com.{gamename}.program/files/saves
2. Backup your saves by copying/moving them to a different place. If you do not back them up, they will be deleted automatically and you will lose all your progress.
3. Uninstall the old version.
4. Install the new version.
5. Place the backed-up save files in the directory that will now be empty:
SD:/Android/data/com.{gamename}.program/files/saves
6. Launch the game.