For cruises that are truly dedicated to exploring Southern Greenland - as opposed to stopping in on the way from one Arctic destination to another - the routing will likely involve a charter flight. Ours was from Reykjavik to Narsarsuaq. (If you want to know more about our Iceland experience, pre-cruise, please check out that storyline, here.)
Narsarsuaq is a tiny little village with a relic of an airport from World War II. Upon arrival, we found bright sunshine and surprisingly warm temperatures, and a series of small buses looping the one mile or so from the airport to the pier. Some of us opted to take the walk through town instead of load up on the bus, as the weather really was that nice.
At the end of the cruise, we had almost a full afternoon to visit the small museum and explore the town itself while we waited for a delayed charter flight to pick us up and return us to Reykjavik.
In subsequent years, as airport facilities are improving around Nuuk and Kangerlussuaq, further north in Greenland, I do expect to see itineraries start to use those airports more often than this remote airport in Narsarsuaq. Ships will then simply have to travel a bit further post-embarkation, to reach their first excursion and exploration locations.