From airport
From the airport it is possible to take the Metro directly from terminal 3. You get off at Kongens Nytorv St. where you can walk to the Phoenix Copenhagen in 5 minutes. 

If you take a taxi from the airport the price is about DKK 250,- All taxies take taxameter and will accept major international credit cards.

From the Oslo ferry
From the Oslo ferry you can take bus nr. 26 going towards Ålholm Plads. You get off at Dr. Tværgade. From here it will take you 2 minutes to walk to the hotel.