Indeed. Opening the 'dmg' image will create a new drive in the finder.
Think of it as putting a cd-rom in the drive. The contents of the drive then appears.
If it's an application, and all you see is the application icon (and maybe a 'ReadMe' file), you can usually just drag the icon to the application folder.
Sometimes an application needs to be installed, and in this case the icon will usually have a '.pkg' extention, or will look like a box being unpacked.
Once you've installed your app, you need to 'eject' the disc image (just click the little eject button next to the dmg in the finder), then you can trash it! (Or, if you're like me, save it for the future in case you need it again)