Download from Mozilla Firefox Developer Edition webpage. Extract it with file-roller and move the folder to its final location. A good practice is to install it in /opt/ or /usr/local/.
Once you moved the files to their final location (say /opt/firefox-dev/), you can create the following file ~/.local/share/applications/firefox-dev.desktop to get a launcher with an icon distinct from normal Firefox.
[Desktop Entry]
Name=Firefox Developer
GenericName=Firefox Developer Edition
Exec=/opt/firefox-dev/firefox %u
Terminal=false
Icon=/opt/firefox-dev/browser/chrome/icons/default/default128.png
Type=Application
Categories=Application;Network;X-Developer;
Comment=Firefox Developer Edition Web Browser.
StartupWMClass=Firefox Developer Edition
Please note, that the parameter StartupWMClass is added to prevent duplicate icons in the launcher, as explained here.
To mark the launcher as trusted, make it executable:
chmod +x ~/.local/share/applications/firefox-dev.desktop
To launch it, navigate to ~/.local/share/applications/ using your "Files" application (ensure you turn on hidden folders), then double-click firefox-dev.desktop. Alternatively, search for Firefox Developer, and simply run the firefox binary, and voilà.
Note that, when you install manually, the F.D.E. does not have the unity global menu by default.
Reference: linuxconfig.org