The .DMG is a Disk Image and you have to unpack it before you can install it. Double click the .dmg file. It should present you with the install graphic. Click and drag right in the picture.
If you don’t have that panel on the left, you can drag the newly created Audacity folder to Go > Applications from the far top menu bar. I’ve done that.
All these places are stand-ins for the OS-X /Applications folder. I do wonder why your graphic install failed. That’s concerning. Are you doing this from the Downloads folder? I do everything from the desktop. I wonder if that makes a difference.