I've just used apache as a hobbyist, so I'm no expert. But yes apache is a program or (in linux you'd call it a "service" or "daemon"). You can install it on any distribution and I believe the configuration file on most distribution is installed to the /etc/apache directory. I personally use debian, but it should be just as easy on whichever distro to use your package manager to install it. Then you just create your html files in the root directory (on debian I believe it defaults to /var/www).
To access your website you can just open a browser on the same machine as apache and type
localhost into the address bar. It should open the default apache page.
Now I'm sure there's a lot more information than that if you want to become a guru or system admin, but for a local home network, that's about it. Try to google for your distro name (looks like you use Suse) and apache setup. Here's what I got from a quick google
http://www.novell.com/coolsolutions/feature/595.html. You should be able to ignore the php and mysql part for now.