Basically the steps as described by iki.
What had confused me before was that after entering my login and password under "DSL" a dialog window appeared asking me to define a password for what Knoppix' called (and what roughly translates from German into) the "default bunch of keys". At the beginning I didn't know what was meant by that. Every time I start the DSL connection another dialog window opens asking whether to allow access to the default bunch of keys (once/always) or not. Also, I wasn't aware that you can choose between the various connections (and connection types) established when clicking the Network Manager icon. To me, that was the most useful hint given by iki.
So once you know how it all works it is really easy.
All this works regardless of ADRIANE being enabled or disabled, at least in my case.

@Harry Kuhman:
It should be mentioned that of course routers can become the target of online attacks and manipulations with a serious impact as well.