Denmark To Amsterdam

There's a direct night train between Copenhagen and Amsterdam.
Depart 6:20pm arrive Amsterdam Centraal Station at 10 am. http://www.citynightline.ch

There are trains that connect the cities: the overnight previously mentioned and various day train options. It's a long trip though, another option is to fly. Probably cheaper to fly and certainly faster.

A night train is always a cheaper way to go as you can substitute a night in a hotel with a night on the train as you're traveling between cities. A friend of mine and his family are taking the night train between Paris and Barcelona this summer as it's about an 8 hour journey.

www.db.de
This is the german train system web site which will help you out. click on the english flag. and just enter where your comming from to where your going. It will show you the different connections possible and the times.