Isn't Firefox on of those apps where the DMG folder actually visually indicates to you to move the app into the Applications folder? With a shortcut to the folder and all? I'm kinda surprised that some people don't get it, though some apps make it even more explicit.Mount the DMG Firefox came in.
Drag the application to your Applications folder (In the hard drive)
Boom. It's installed. You can unmount the image and delete the DMG.
That's how you install a large percentage of Mac apps. The tiny rest of them use actual installers. They will always say "install" on them. The rest are installed via drag and drop.