I have been around some of the guys from Air Greenland, but haven't worked there myself.
There are two main bases, Nuuk/BGGH (where the headquarters are located) and Ilulissat (BGJN). The roster is 3 weeks on / 3 weeks off.
If you are a DHC8 pilot, a typical day might consist of 6-8 sectors flying between the small airfields on the West coast with an occasional trip across the icecap to Kulusuk (BGKK) and Keflavik, Iceland. Generally they have 1 off day every week while on duty.
The Kingair pilots have the same roster system but that aircraft is only flying as an air ambulance so the number of sectors per day can vary somewhat.
Pilots on the Airbus A330 are all based in Denmark as far as I know and operate the daily service between CPH and SFJ.
Many of the pilots live around Scandinavia and commute regularly between Denmark and Greenland, but some also opt to live in Greenland (mainly in Nuuk), especially those who are local to the area.
It is a very friendly bunch flying in some the most demanding conditions one can encounter, but on good day the views are out of this world and the compensation is very competitive from what I hear!