In short: the answer to your question is just in the page you posted.
If you like to install and update Webmin via APT, edit the
/etc/apt/sources.list file on your system and add the lines :
deb http://download.webmin.com/download/repository sarge contrib
deb http://webmin.mirror.somersettechsolutions.co.uk/repository sarge contrib
You should also fetch and install my GPG key with which the repository is signed, with the commands :
apt-key add jcameron-key.asc
You will now be able to install with the commands :
apt-get install webmin
Long version. If the package was installed with dpkg the it is installed. Once installed apt-get can handle it, i.e. you may run
sudo apt-get remove webmin to uninstall it, or
sudo apt-get install -f to fix the dependencies.
Just to be clear,
dpkg. In a very short simplificated way, dpkg is the engine behind apt-get (and aptitude), it's the guy leading with the actual installation of packages directly and, of course, is potentially harmful to your system if you mess up, whilst apt-get really take care of you trying to avoid any disturbance that dpkg may generate. :)
Going to the point, the first part of my answer reply to you directly, the alternative to install a .deb with dpkg is to add a repository. Why, well in the repository you will catch every update of the program, while with dpkg your version is fixed. Also, in theory, the repo may solve all your dependencies automatically. In dpkg is allways convenient check for broken packages afeter the installation with
sudo apt-get install -f.
Adding a repo consist on four steps: add the address of the software source, add the key to make ubuntu able to trust the source, update the database, and install. All of them are above. Adding a ppa saves you the steps 1 and 2! Cheers!