You travel to Visby by air via:
Stockholm Arlanda (int. & domestic flights)
Scandinavian Airlines
+46 (0)8 797 40 00
You travel to Visby by ferry-boat via
Nynäshamn (70 km south of Stockholm) or
Oskarshamn (Southeast Sweden) with
Destination Gotland
+46 (0)771 22 33 00
Other info about Gotland: Gotland.net