Translation:The prince says to the servant, that he would like to read the newspaper tomorrow.
In the main clause (here it is "Prinsen siger til tjeneren") the word order is verb-adverb, in the subordinate clause ("at han gerne vil læse avisen i morgen") this is then swapped. This PDF has all the basics on Danish word order and goes into a bit more detail with what I just said and for even more detail on word order click here and scroll down to "Word Order"
thanks, Xneb. so just to check: usually in main clauses (at least, in main clauses that start sentences?), the word order is subject + verb + adverb ("han vil gerne"). but in subordinate clauses, word order is always subject + adverb + verb (which is why we have "han gerne vil"—but it could also be "pingviner ikke flvyer," or whatever). right?
It sure is. It modifies the manner of the vil læse construction here, shifting it from "want to/will read" more to "like to do the reading". English doesn't have a comparable adverb, which makes proper translations a bit harder.
Det gør jeg - I will do that.
Det gør jeg gerne. - I like doing that. / I will do it with pleasure.
"Servitrice"? My best guess is that servants have been mostly male in historical times, and waitresses only became a thing with a bit of international influence. French, in this case. For some reason calling male waiters tjener stayed through that influence. (You can call waitresses tjener as well, of course. The Danes aren't big on gender splits.)
In my opinion, a better English translation is, "The prince tells the servant that he would like to read the newspaper tomorrow." You would use the verb "says" more often as the intro to a quote. "The prince says to the servant, 'I would like to read the newspaper tomorrow.'" However, you accept "tells" already anyway, so you're a step ahead of me!