Most flights land at kangerlussuaq, one of those lovely places on earth where you can buy duty-free after landing. stock up on cheap booze, smokes and everything else at prices far lower than the rest of greenland. important: greenland is not a member of the eu, so although you may be travelling from denmark, the custom rules are the same as for a trip out of the eu.
These are the names to look for, if you need to buy groceries:
Pilersuisoq - Chain of larger supermarket usually found in small villages. Has a little bit of everything.
Pisiffik - Chain of larger supermarkets present in the cities.
Spar - Dutch supermarket chain with a few shops in Greenland.
Brugsen - Danish supermarket chain with a few shops in Greenland.