As mentioned on https://appimage.org/ the recommended way to run an AppImage is to
Make it executable
$ chmod a+x Subsurface*.AppImage
But, I for one am having a hard time remembering this, and I can't be the only one? I find the recommendation quite user-unfriendly because it requires using the terminal.
The following page explains a way to do this without the terminal. https://itsfoss.com/use-appimage-linux/ Right clicking the AppImage, going to Properties, going to Permissions and enabling "Allow executing file as program". Then it should be possible to simply double click the application to start it.
But, this "Allow executing file as program" option doesn't seem available in ElementaryOS. And when attempting to open it (even after making it executable using chmod) I get the Select Application window.
Update: I'm not sure why but after downloading and running the Subsurface AppImage I can also simply run the Cura AppImage...
What is the recommended, non terminal, way to use AppImages in ElementaryOS?
The specific AppImage I've tried is Ultimaker's Cura, from: https://ultimaker.com/en/products/cura-software
This Blueprint might be relevant? https://blueprints.launchpad.net/elementaryos/+spec/appimage-integration