Double-click the file FirefoxVx.y.dmg in your Downloads folder
This results in a window similar to the picture at the top of this page
Do NOT drag the application icon to the folder icon. Instead:
Make sure Finder is the frontmost app (type ⌘+space, then finder, followed by a carriage return)
Select Go to Folder... from Finder's Go menu (2nd item from the bottom of the list), then type ~ in the resulting dialog box
If there is no Applications folder in the resulting window:
Create one by selecting New Folder (2nd item from the top of the list) from Finder's File menu
This will create a new folder named untitled folder Right-click on the new folder, select Rename (4th item down) and type Applications followed by a carriage return
Drag the Firefox icon from the window that resulted from steps 2 and 3 above to the Applications folder in your user space (aka your home directory)