Once you donwload the DMG image, open it and follow the instructions. All you need to do is drag the app icon to the Applications folder.
See Installation Support page for more information in case of any alert or trouble!
The application will notify you of any updates, unless you disable the update feature manually. Check the Preferences once you run the application. If the update feature is enabled, the application will automatically update upon your confirmation.
In any case you can check this website for the latest release and update Sail Replay manually.