Train communication in Sweden is often used for traveling in the country as an easy and relatively cheap way to travel. The prices of train tickets vary greatly depending on when and where you travel. 

The nation wide train company is called SJ and through them you can book tickets for everywhere in the country. As a full time student you should have a little 'SJ' mark on your nation card, and through that you can get a student discount when you buy your tickets. You will need to show your card when you are traveling with a discounted ticket. 

Keep in mind that cheap tickets can be found in two ways: one is to book your ticket long in advance. The other is to keep an eye out for last minute tickets. 

You can find SJ homepage here. On their homepage you can find information about tickets, book tickets, information about special offers etc.