Wth a .run file, you normally just have to run the file. Since they're talking about sudo, you probably want to run the file as root.
First, right-click on the file and make sure that the file is executable (under properties/permissions).
Next, open a terminal. Running commands as root is dangerous, so they don't tend to make it easy.
If you have sudo configured (most systems do) then you can type: [Note the capital ‘D’]
Otherwise, you can do:
su -c '/home/username/Desktop/filename.run'
This assumes that your desktop directory is /home/username/Desktop
. You can check this by right-clicking on the desktop and looking at the paths option.
Either way, you will need to type in the root password when prompted.