If you downloaded the .tar.bz file from Mozilla open it and you'll find a directory called thunderbird. Put that wherever you please. Inside that is the executable itself, also called thunderbird. Let's say you put the thunderbird directory straight in your home directory. To run it open a terminal any type ~/thunderbird/thunderbird. You could also find it in your graphical file browser and double-click it. When you know it works you can make a custom launcher for it in the menu and/or on the panel, though how will depend on what distro and desktop environment you use.