Hi llatort,
It depends on where you are traveling to and from, how much time you have and what you want to see. For example, there are 2 direct trains per day between Oslo and Stockholm, one in the morning and one in the afternoon, taking a little less than 5 hours. Other trains involve a train change in Göteborg and take about 7.5 hours. Prices vary greatly, depending on how far in advance you book, anywhere from 225 SEK ($26) for an advance-purchase, non-refundable ticket, to 1200 SEK ($140) for a fully-refundable, walk-up fare. You can find schedules, and book tickets online ahead through the Swedish Rail website - www.sj.se
It's certainly common for people, both tourists and locals, to take the train, especially when compared to train travel in the U.S. but not as common as it is in countries such as italy or France. It's a pretty trip, across the width of Sweden through the heart of the lake country but it can be cheaper and faster to fly (1 hour flights from $50). See www.skyscanner.com for options. If you have a lot of time and wanted to stop in several places along the route, such as Göteborg and somewhere in the lake country before ending in Stockholm, then the train would be a better option.