What is the best and chepest way to go from kopenhak in Denmark to trondhiem in Norway?

prefer to go by train.

The only way is by ferry. Initially by train, then train goes inside the ferry then you'll be having few hours fun on the ferry till you get to Norway.

This is the only way and very fun way of getting to Norway beside by air.

When i was living in Denmark in 80's, the fair cost was around 400 krone's which was the cheapest way. good luck!

I'd check out this site: iBtraveling.com and compare prices with trains and planes. Then you'll know what way is cheapest.

Trondheim Airport V忙rnes (TRD) is the closest airport to Trondheim and is located in Stj酶rdal, about 30 kilometers to the north-east of the city center. The airport offers regular domestic flights to and from most major cities in Norway, as well as daily flights with service to a few European cities.

There are moreover 3 daily direct flights from Copenhagen to Trondheim with Wideroe (http://www.wideroe.no/english/index.html ) (collaborating with SAS Braathens)

Here are links to the train planners of Denmark and Norway.
http://www.rejseplanen.dk/bin/query.exe/...
http://www.nsb.no/home/

I did a trial search with the train planners, you need to 'break' the travel, I did search to Oslo first, takes about 10 hours if you use a day-train, and 14 to 18 hours for an overnight journey.
Oslo to Trondheim will take an other 7 or 8 hours, not counting the time you will need in Oslo between the trains.

If you have the time, stay a day or longer in Oslo, I liked the town.
I did not check prices, they might be high!
Flying is often cheaper than this kind of long distance trains.

If you can not get your train tickets, or if they are too expensive, here is a link to a bus company:
http://www.eurolines-travel.com/ Denmark only, I did not find a link for Norway.