By hotbar I am going to assume you mean the Dock, the thing that sits on the bottom of the screen (by default) and holds applications and other such things.
Alright, here is what happens.
You download Firefox.dmg (dmg = Disc iMaGe)
You double click it to mount it to your system.
Within this is an icon, the icon (if I remember correctly) has a little arrow next to it that points to your Application Folder (Since Mozilla is lazy, this is just a picture, nice developers have a shortcut to the Application Folder there)
See that little Lozenge in the upper right of the Finder window? Press that to reveal your toolbar and Sidebar.
Drag the Firefox to the Applications icon on the Sidebar of the Finder window.
You will now experience a period of nothingness as Firefox is installed.
Now click in the middle of that window containing the Firefox icon, so that nothing is selected, and press Apple+E.
Navigate to your Applications folder and then you can drag that firefox icon to the dock.
The system is a little confusing when you are used Windows, but in the end makes a certain degree of sense, and the advantage is that the whole application is contained in that icon, in fact when you view that in any other OS, it shows up as a folder.
Bear in mind that this is not necessarily a function of the File System as it is of the OS. In fact, truthfully, if you wanted you could drag the Firefox icon anywhere on your system since OS X uses symbolic links and other really fancy, really good things for handling file locations. This is why file moves are pretty much instantaneous, regardless of size, and you can rename files while they are being used.