For feeling like you have to live in a German fairy tale. The cat one would be the Haustierbesitzerverbrennungsprozessbeobachtung, the other would be the Märchenschreiberangststörung. Silly, that's German 101!
It's simple, you use 'der' when using 'the' is appropriate. 'Die', on the other hand, is equivalent to 'the' and takes those places instead. Then comes 'das' which means 'the' and you can just map that to its English equivalent.