If you use Debian, Ubuntu, or another distro which uses deb packages, you can download the deb (weather-wallpaper-0.2.0.deb) and simply double-click on it to launch the installer, or you can add repository to your sources.list file, so that your distro can inform you of new releases.
If you choose for the second method, open the file /etc/apt/sources.list with your favorite editor as root and add this line:
deb http://ppa.launchpad.net/zootropo/ubuntu hardy main
Update the list of packages writing sudo aptitude update on the terminal, and install the application by writing sudo aptitude install weather-wallpaper.
If you use other distribution, download the tar.gz: weather-wallpaper-0.2.0.tar.gz, uncompress it, and execute the command make install with root privileges.
To start the program run Application -- Accessories -- Weather wallpaper.
The program will retrieve the weather report from NOAA and create a wallpaper with the information for the default location: Getafe, Madrid, Spain. To change it to your current location, right click on the status icon and select preferences, where you can specify the ICAO Location Indicator for your city and select the unit system you want to use.