The Swedes have an expression that the Danish language is like "Swedish with a hot potato in your mouth", but from my mouth, the Danish language makes some very odd sounds like an animal farting, or Vogon Poetry, or something.
I've had about twelve lessons so far. The good news is that I can now read and understand some things. But when people are speaking it is like have a radio with dodgy reception: If they're not going too fast I can pick up maybe 10-20% of what they're talking about, but conversation is going to take some time. That's fine - Most worthwhile things take some effort, but it is a bit humbling when you're starting out :).
Another interesting observation by my teacher (and others) is that you actually make mistakes in the last language that you learned, so I'll say things in German (which I learned, well, ages ago) when I meant to say them in Danish. This is interesting because I'm trying to find a phrase, and my brain responds with "here's that phrase the last time you learned a language" and out it comes - in German! This is probably different than children learning a language who can just associate a word with a thing directly and can move fluidly between languages. They have no such redirection.
Anyway it is a good thing that they're all so good at English here... it takes some of the pressure off having to learn Danish quickly, although I wish I could!