how do I launch firefox after installing it?
You can drag your new Firefox Application directly to the Applications folder.
The folder shown on that blue window is for convenience, a 'shortcut' to your own apps folder. 

Either way, you need to drag the actual Firefox app [Application, though the .app is hidden by the system, like on Windows], not its container the .dmg file.

A .dmg is a convenient &amp; secure method of getting an app to you from the developer. It is a self-checking structure, so it knows if it was downloaded correctly &amp; won't open if it's broken. It's a bit like a zip file except that you can 'see' straight into it without unpacking to a new folder…. but like a zip file you need to get the contents out of it before you can use them.

Think of a .dmg as having 3 'stages'… 


stage 1 - the original .dmg file - when you double click that 
stage 2 - it mounts a virtual disk on your desktop, which will open to show something along the lines of your blue window.
[They're not always as nicely set out as that one &amp; they don't always open automatically, sometimes you have to double-click the virtual disk to open it]
stage 3 - You then take the contents [your shiny new app] &amp; either drag directly to your Applications folder or a convenient shortcut in the same window.
Sometimes you need to double-click that 'application' to launch a separate installer.
You will [almost] always be told which to do.


Once the Application has copied itself to the Applications folder, you then can 'put away' the virtual disk.
You can do this by dragging it to the trash. Disks are not erased by dragging to trash on Mac OS, they are ejected.
Alternatively, you can right click &amp; Eject, or select &amp; hit  Cmd ⌘   E  

If you want your new app to have a place in the Dock, you can now drag the version in your Applications folder to the Dock &amp; it will add to it.

Once you're happy it all worked, you can delete the .dmg file 

 Sorry if this explanation is over-simplistic - I just thought it deserved a canonical answer