There currently is one option to travel by night train from Copenhagen (Denmark) to Prague (Czech Republic), taking approximately 12 hours: Namely the RJ 387. These lines are operated by Deutsche Bahn, DSB and České dráhy.
Deutsche Bahn (DB) exited the actual night train business in 2016. However, it operates around a dozen Intercity and Eurocity trains that run exclusively at night.
In these night trains, there are only first and second class seats. The lights stay on all the time and there is no way to recline the seats.
DSB (Danske Statsbaner) is Denmark's national railway company, operating passenger trains across Denmark as well as connections to neighboring countries.
ČD, the Czech national railway, operates domestic and cross-border passenger trains linking the Czech Republic with its neighbors.