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