On Sunday I reached a happy milestone as a new citizen--I voted for the first time in Sweden!
EU parliamentary elections were held, albeit with a disappointing turnout continent-wide. The process was similar to how I've experienced it in New York, except that you use little sheets of paper, a different sheet of paper for each different party. Here's the slip of paper for the Moderate Party (conservatives):
I've found political culture here to be superdifferent from the US, where people are very vocal and public about what parties and political issues they support. Here, it seems to be the height of rudeness to ask whom people are voting for, and you certainly don't see any bumper stickers around town.
So if you don't want other people to know how you're voting, you take a whole bunch of different slips from different parties. Then you go to an unsteady privacy tent-thingee where you mark your vote on the party of your choice, put it in an envelope they provide you, and hand it in.