The process is pretty straightforward, just grab your passport, a valid driver's license, and a credit card with enough available balance for the security deposit they block at pickup. Most places include basic third party liability by default, but a collision damage waiver will cost extra and save you a massive headache if you clip a roadside rock on those narrow backroads. You can scope out plenty of options for car rental in Sweden through aggregators like this one
https://getrentacar.com/en-US/sweden .