I did install wordpress using the distributed zip archive following the detailed instructions on the wordpress site. Setting up the database and editing the PHP config files was no problem.
The installation went smooth and everything was working as expected.
Problem 1: Configuring Multisite
Multisite is a great feature of wordpress. It gives you the ability to create more than one site (or blog) within your wordpress installation.I did the setup using this step-by-step guide. So far so good. With my new multisite feature enabled I wanted to create a new site and filled in the necessary informations for it. The creation succeeded without an error and when I clicked on the dashboard of the newly created site I got a "Page Not Found" error.
Hm ... googling around I didn't really find a good answer.
I decided to check the network administration guide of the wordpress documentation and found a really helpful paragraph about using mod_rewrite (multisite feature needs mod_rewrite) and Apache Virtual Hosts.
My Apache installation is using virtual hosts so what finally did the trick was to add these lines to my VirtualHost section:
<VirtualHost *:80>
<Directory /var/www/vhosts/wordpress>
AllowOverride Fileinfo Options
</Directory>
Problem 2: Changing the domain name (or change the URL)
I am using DynDNS and I (and my users) want to access the wordpress installation from the internet. During the installation I did not realize that this was so important, because I thought I can change it easily afterwards. Well, changing it in a Non-Multisite environment is easy, but it turns out that a change of the domain name in a multisite installation is a little bit harder.What helped me a lot was this documentation on the wordpress site.
Because my installation was totally fresh I skipped the step to make a backup of my database. I walked through all tables of the database and replaced every occurrence of my old domain name with the new DynDNS domain name.
Finally I changed the DOMAIN_CURRENT_SITE attribute in the wp-config.php file to point to the DynDNS name as well and after that my multisite wordpress installation was accessible via the DynDNS url.
I can't say whether it would have been easier to change the domain name before I activated the multisite feature, but it would make sense to me.
Anyway, it works now.