Within RM9, select the Home panel and towards the bottom right, there is an update section. That tells you whether or not there is an update, or just that you are at the latest update. There will also be an ‘alert count’ in red against the Home name/icon at top right, trying to draw your attention to new items on the Home panel.
If there is an update, select it and it downloads a new DMG - disk image file - then closes RM, and mounts the DMG file on the desktop. Included in the display of the contents of the DMG file is an icon for the RM application, and you drag that into the Applications folder within Finder. You are asked whether you wish to replace the existing version of RM, and you need to agree to that.
You can then eject the DMG image and you can also close a spurious pop-up saying a file can’t be found. The latter is a bug that has been there since the very earliest days of the beta of RM8.