Get a valid passport from the nearest passport agency in your region of the U.S. All international travel requires a valid passport regardless of visa restrictions. You must have at least two blank pages for the entry and exit stamps.
Gather together your entry and exit plans for Sweden. You need a copy of the return ticket for when you leave Sweden to show that you do intend to leave. If you do not have a flight back to the U.S. from Sweden, you will need proof of exit from Sweden such as a different flight itinerary.
Bring proof of finances such as a bank card or current credit card. Sweden needs to see that you have sufficient funds to pay for lodging and expenses while in the country.
Write down the name and number of the hotel you plan to stay at when you first arrive. You need to show you have somewhere you plan to stay.
Proceed through the customs line when your flight lands in Sweden. Present the agent with all your documents and a valid passport and they will stamp your 90-day stay in a blank page of your passport.