As an expatriate from an EU-nation living in Sweden you have the option to vote in the Swedish elections for the European parliament instead of in your native country.
To vote in the Swedish elections you need to be at least 18 years old on the 25th of May which is the election day for the EU-election and be registered as a resident in Sweden no later than the 25th of April. In addition to these two requirements you have to register to vote, this is something unique for you as a non-citizen as Swedish citizens are automatically registered to vote.
You will need to register for voting by filling out a form that should have been or will be sent to you by the Swedish election authority during March or April. In case you have not received one, you can download the form here.
The form is in Swedish but here is how you fill it in:
If you prefere to get the form in your native language, call the election authority at 020-825 825.
The filled out form need to be sent to your county administrative board or länsstyrelse in Swedish. The address for Stockholms country administrative board is:
Länstyrelsen I Stockholms län
104 22 Stockholm
The addresses of the other country administrative boards can be obtained here.
The county administrative board will then add you to the election roll and send out a voting card. Remember that in Sweden there is an early voting system that will allow you to vote up to 18 days in advance of the election day. You can vote early anywhere in the country, all you need to do is find a polling station present your ID-card as well as your voter card.
To vote you simply pick a ballot of the party you will vote for, enter a voting both where you place the ballot in en election envelope. Then you hand over the envelope to the electoral official together with your voting card and ID. Up until this point the procedure is the same whether you vote early or not. If you vote early the election official will take your voting card and election envelope with your ballot and put them in an envelope, this will then be mailed to your local polling station where the vote will be registered and your name crossed of the election roll.
In the municipality of Järfälla the early voting stations can be found at six locations, you can find maps and opening hours by clicking here.