The airline suggestions are good. If you are on a tight budget, you might consider taking the bus, which will run about 50$ one way. Plus you'll save on the bus from Stockholm aiport (Arlanda) to downtown, which if I beleive is around $10.
The downside is that the bus takes about 9 hours. But, if money is a concern, you could take the night bus and save a night's accommodation. You can get info at:
http://www.swebus.se/SwebusExpress_com/