To get from the airport (located in Vágar) to Tórshavn, you will need to either take a taxi, airport shuttle, rental car or bus.
The bus route is number 300 (it says Tórshavn on the front), and the schedule can be seen here.
A list of taxi services can be found here.
As a special discount to participants of SCANCYPAA, Bilrøkt is offering a 25% discount on any rental car they have available! Just mention to them that you will be attending the conference and they will be happy to help. A link to their website is here.
***PLEASE NOTE: RENTAL CARS ARE AVAILABLE FROM TÓRSHAVN ONLY AND NOT DIRECTLY FROM THE AIRPORT