A .dmg file is a compressed file similar to a .zip allowing a quick download of an installer. Have you checked your desktop for what appears to be an icon of a drive or DVD? Check your download folder where the .dmg is located.
Is this .dmg from a download from a trusted site? It could very well be corrupt or empty (no files in it).
You can try using Disk Utility to force open the .dmg. If there is a problem with that file, it will tell you.