The company that owns the ferries is Destination Gotland where you also book your tickets: Swedish, English and German.
Flights from Arlanda, between Stockhom and Uppsala, to Visby Airport: 45 min. A little bit faster from Bromma in Stockholm.
By car from Stockholm to Nynäshamn and then the ferry (with car) to the harbour of Visby: totally 5 hr 20 min. Included is the time it takes to be in Nynäshamn to get the car on the ferry. The differens between taking
the fast ferry and the slower ferry in minimal, 10-15 minutes, because of speed limitations in the archipelagos. The boat trip itself takes between 3 hr 30 min and 3 hr 40 min depending on which ferry you choose.
If you are travelling light, take the bus from The Central Station in Stockholm to Nynäshamn and you will arrive in time.
It's also possible to take ferries from Oskarshamn (not shown on the map) close to our neighbour island Öland. It's better if you come from the south part of Sweden. During the summer are flights from several destinations to Visby Airport.
Use "DIRECTIONS" up in the left corner of the map. There you can type From 'Nynashamn' and just click the button (the magnifying glass) or to "Visby Hamnterminal". By air 'Arlanda Airport' to 'Visby airport.
If you want to save some time: Bus/train to Stockholm Central Station: From 'Bromma airport' to 'Visby airport'.