If you want to travel from Berlin to Copenhagen (or the opposite way) there are several cheap options. Which one you should choose depends mostly on how much in a hurry you are, how many days in advance you book your trip and how much luggage you have:
The first and fastest option is a cheap flight with easyJet from Schönefeld airport to Copenhagen airport. This takes 1 hour plus about 1½ hour in transfer times one way. Of course you need to include the hour you need to be in advance at the airport. Price for the whole trip is 25 euro for the flight plus 5 euro total for both metro transfers one way, booking- and luggage fee is additional for the flight. The flight ticket should be booked around two weeks in advance, and less then one week in advance can be difficult to find a good price for the flight.
The second and cheapest option is to go by bus from Berlin ZOB am Funkturm to Copenhagen Ingerslevsgade (near the center) with the company BerlinLinienBus. This takes abous 7½ hours plus the half hour or so the transfer to the Berlin bus station takes. Price for the bus trip is from 23 euro and on top of the bus price you will need 2 euro for the metro to the bus station (ZOB) in Berlin.
Another good thing with the bus is that you can bring a lot of luggage for free. Sometimes you need to pay 1 euro extra per luggage though. The buses also have free WIFI (only on German side), personal electricity plug, a lot of leg space, toilet and free water. Included in the price is a 1½ hour ferry ride where you also can get some expensive food and stretch the legs.
Flight from Berlin to Copenhagen
30 euro, 3½ hours, 1 hand luggage (56 x 45 x 25 cm)
Bus from Berlin to Copenhagen
25 euro, 8 hours, “unlimited luggage”