Sweden has a modern and extensive railway system, which connects major cities with frequent and fast services, as well as provides local connections to smaller towns and villages on many regions.
There are international connections to all neighboring countries. From Sweden you can travel by train to Copenhagen in Denmark; Oslo, Trondheim, and Narvik in Norway; and Haparanda just by the Finnish border. There are also night trains from Stockholm to Hamburg and Berlin.
All operators sell tickets to all trains, including the ones of other operators. The prices are the same across all operators' websites. Since SJ is the biggest operator, the easiest way to buy all tickets might be through SJ's website, which naturally gives you the best information of SJ's own trains.
You can also buy tickets straight from Resrobot, which is a publicly owned and maintained neutral service. Resrobot is the system in the background anyway, regardless of the operator from whom you choose to buy your ticket.
On longer journeys with multiple operators it's sometimes easier to search for the trip in two parts. For instance, if you search for a trip from Stockholm C to Haparanda, and if you don't get any results without regional buses and several interchanges, search for Stockholm–Boden and Boden–Haparanda separately.
You can search for all operators' train times through any operator's website. DB's search engine also works in Sweden and is handy, especially when searching for international journeys.
PDF-timetables, containing all scheduled traffic by line, can be downloaded from Resrobot's system (Swedish only).