NSB is the Norwegian state owned train-company and operates all of the train services in the country.
There are train connections between most Norwegian cities, both big and small. Their cheapest inter-city tickets
(minipris tickets at 249kr) are based on demand and availability and will be harder to get for high-season and popular destinations.
Booking in advance as early as possible is a big advantage and will increase your chance of getting these cheap tickets. The minipris tickets can even be bought for the longest destinations, e.g. Oslo-Stavanger, Oslo-Bergen.
The trains are modern and comfortable no matter what class you choose to travel on. However, for longer journeys at night you might want to book a sleeper (NSB sove) which will increase your costs.
For further information about train times/prices/stations/services and to book tickets, go to www.NSB.no, the site can also be viewed in English.