Gather all of your documents and identification to acquire your passport. You need a copy of the front and back of your driver's license, your birth certificate and your driver's license. Download and fill out form DS-11 from the U.S. Department of State website.
Go to a passport photo shop and take passport photos for each person who will be traveling. Passport photos should include a white background, be a full head shot, be colored and be 2-inches by 2-inches in size.
Take all of your documents and your passport photos to a passport service center. Passport centers include many post offices, but check the Department of State's website under the link "Passport Acceptance Facility" for the closest passport service center in your area. Pay the applicable fee which is $165 in 2010. Note that you only need a passport and not a Visa to travel to Sweden and you may enter other bordering countries such as Norway without having to show your passport again as Sweden is part of the Schengen Agreement with the United States.
Determine your method of travel by deciding whether you will travel by air or sea. Airlines that fly to Sweden and Norway include Continental, Delta, SAS and Air Berlin, while cruise ships that dock in the Swedish and Norwegian areas include the Norwegian Cruise Line and Princess Cruises. Factor the cost, length of time of travel and the type of vacation you desire when making this decision.
Arrange for transportation from the airport to your destination if applicable. Choose to pay for a taxi at the time of booking your flight for the most direct route. Other options are to take the train or bus transfers from the Stockholm airport.
Arrange lodging if necessary. Stay at the Nordic Light Hotel in Stockholm for the hotel nearest the airport. Stay at the Raddison Blu Airport Hotel which is actually connected to Oslo Airport in Norway. Use a hotel comparison site such as Hotel Pricebot to compare prices and attractions especially if you are staying in a less populated area in Norway or Sweden.
Pack appropriately, remembering the cold weather that is often in Norway and Sweden. Pack for warmer weather if you will be traveling during the summer. Pack a thick coat, water proof jacket, thermal underwear and clothing that can be worn in layers to combat the cold weather. Do not forget the sunblock and your camera to capture important images during your travels.
