I plan to order a small VPS. Because of my little budget, it has only one Domain included in it's package, but I would like to move two of my domains to the VPS. So my solution would be like this:
say i own "test.de" and "example.de"
I move "example.de" to the new VPS and run the content from the old "test.de" as subdomain of the VPS "test.example.de"
Is there a way to redirect from my old webserver, that users can use "test.de" but the contents are fetched from test.example.de? And also search engines should display search results for "test.de" and not the subdomain.
Your VPS will come with some kind of operating system (such as CentOS), and optionally a control panel like cPanel ($$$) or you can install one of the free control panels, Webmin or Kloxo.
The control panel will make it easy to set up both domains, in their own accounts, on the VPS. You can also do this from the command line, but its harder.
Your VPS will have one or two IP addresses also. You will need to either use those IP addresses for a name server on your DNS or use an independent DNS service. The DNS service will have the records for your domains that reside on your server. The records say "Hey, that domain name is really hosted on this IP address: xx.xxx.xx.xxx", pointing to your VPS IP address.