The only way to reach Christianso is by ferry from Bornholm. Christiansoefarten runs a passenger boat from Gudhjem on the north coast of Bornholm year-round, with the journey taking just over an hour each way. In summer there are several daily departures; in winter the service is reduced to a few times a week.
Most visitors come on a long day trip — the morning ferry over, lunch on the harbour, a walk round the fortifications, and the afternoon ferry back. To stay overnight you will need to book the single guesthouse well in advance; there is no camping and no other accommodation.
To get to Bornholm itself, take the fast ferry from Ystad in southern Sweden (about an hour and a half) or a flight from Copenhagen to Bornholm's Ronne airport (35 minutes).