The island of Utö is in the Stockholm Archipelago South East of Stockholm. We suggest you fly to Stockholm.
From Stockholm Arlanda Airport you can take the Arlanda Express train to Stockholm City Centre.
From the Stockholm Central Station you can take a subway and bus to Årsta Brygga, where the ferry to the start on Ornö leaves. Use the travel planner in this link and put in Stockholm C as your departing station and Årsta Brygga as your arrival station. Spectators, friends and family can take the regular ferries to Utö.
If you arrive by car there is a big parking lot at Årsta Brygga where the ferries leave from.