Bus 67 takes you to Skansen via Karlaplan. The metro station at Karlaplan is served by the red line to Ropsten.
From T-Centralen in the city centre you can take bus 69 or bus 69K and change to the No.7 tram at Norrmalmstorg, Nybroplan, Styrmansgatan or Djurgårdsbron. The tram takes you out to Djurgården and stops at Nordiska museet/Vasamuseet/Junibacken, Liljevalchs/Gröna Lund, Skansen, Djurgårdsskolan and Waldemarsudde.
From Slussen you can take bus 76 (destination Frihamnen or Ropsten) and change to tram No.7 at Nybroplan, Styrmansgatan or Djurgårdsbron.
The ferry leaves from Slussen at the end of Gamla stan. The ferry takes visitors to Skeppsholmen and to Allmänna gränd on Djurgården. The nearest bus stop in Gamla stan is Räntmästartrappan. Bus 2 and bus 76 access the stop. The ferry terminal is a short walk from the Slussen metro station.
Going by car is not recommended since it´s difficult to find parking space on Djurgården and traffic is quite heavy during rush hour.
Skansen is not very far from the center of Stockholm. Walking here gives you a very nice tour of the Stockholm waterfront.