How do I install an application from a .dmg disk image?
Applications that are distributed on disk images (.dmg files) are designed to be installed using drag and drop. You can safely drag and drop the application from the virtual drive into your Applications folder and use it from your Applications folder. After copying it to your Applications folder it's safe to eject the virtual drive and delete the disk image file.

Nearly all applications will work just fine running off that virtual hard drive as they store their content in your user folder (eg. browsers, mail applications, etc.). It will however stop you from running application updates as the disk image is read only.