A "*.dmg" is a disk image file.
Opening the image (double-click) means some program reads the data
and mounts the "disk" filesystem.
Look for your app inside the mounted volume, and copy it (the app, docs,
etc) where appropriate.
When the copying is done, eject/unmount the disk image.
Save the image file if you want to, or just throw it away.
(i.e., No, don't mount the image every time to run the
program on it. In fact... wedon't do that at all, usually).