Trondheim is easily accessible with any kind of transportation.

There exists daily trains between Oslo and Trondheim provided by NSB (Norwegian State Railways). The travel takes about 7 hours.
Trondheim is also connected by train with many other norwegian cities.
Website: NSB

The city is connected with direct flights with a number of European destinations including Amsterdam, London, Copenhagen, Stockholm, and Oslo.
For more details check the airport website: Trondheim airport

Trondheim is located along the main norwegian highway, E6, that connects Oslo with the northern part of the country.

The Trondheim Værnes airport (TRD) is located about 30 km north of the city center.

Two companies operate between the city and the airport, Flybussen and Værnes-ekspressen. Both of the them stop near all the main hotels in the city and not too far from the university and depart every 15 minutes from the airport. You can board the buses just off the arrival area of the very small airport. This is by far the best and most economical way to get to Trondheim.

The travel time is approximately 30 minutes, depending on the traffic and on the bus stop. Værnes-ekspressen (grey buses) is an express so gets to town faster and more directly. If you're coming for there first time to the area and during visible daylight, try to sit on the right side of the bus to see the spectacular Trondheimsfjord all the way into town.

Trains depart hourly from the airport, the travel time is approximately 35 minutes. The train station is walking distance from the airport arrival terminal and in the city center in Trondheim.
Website: NSB

The taxi stand is immediately in front of the arrivals terminal. Note that is far more an expensive option than the buses and unlikely to get to town any faster.
Trønder Taxi - Phone: (+47) 07373
Norges Taxi - phone: (+47) 08000
Stjørdal Taxi - phone: Phone: (+47) 07483