If you are away on the election day, or just want to get it over with, you can vote ahead of time. The Swedish verb for early voting is förtidsrösta.
There are quite a few places where you can vote ahead of time, and the important thing is to bring your "röstkort" (voting card) and your identification. Sometimes even just your identification card or passport seems to be enough!
The website val.se will list places where you can förtidsrösta. When you bring your voting card it's also often possible to vote early in a municipality that isn't your own.
Trivia: When counting votes, the early votes (and votes from abroad) are the last to be counted. This is because people actually can change their minds and vote on the election day, hence dismissing their early vote which then won't be included in the count.