It would help if you give some more detail on what sort of help you’re looking for. What routes have you found so far? Are you looking to make the journey as quickly as possible, or spend days or weeks getting there?

It’s a long day’s travel, routing via Frankfurt. You can also take a short journey to Offenburg, and pick up a sleeper train to Hamburg.

I was thinking about a 10 days trip, I would like to stay in Copenhagen during few days, maybe also visiting Prague few days. I’m not a fan of long journeys in train, 5 or 6 hours maximum. 

Prague is well out of the direct route to Copenhagen.

But since you have a few days to get there, you might travel to Basel then through Switzerland and Austria to reach Vienna, then Prague. In my opinion, that’s more interesting than the direct route across Germany. There are plenty of places you could stop.
 

Alternatively there is a sleeper train from Zurich-Prague, which calls at Offenburg.

 From Prague, you continue to Berlin, where you can pick up trains to Hamburg and Copenhagen. There’s also a sleeper from Berlin to Copenhagen in summer.