Greenland  (Greenlandic: Kalaallit Nunaat; Danish: Grønland) is the world's largest non-continental island, in the far northeast of North America, largely within the Arctic Circle. Although it's still part of the Kingdom of Denmark, it was granted self-government effective in 1979, with Copenhagen remaining responsible for its foreign affairs. The closest neighbouring countries are Iceland to the South-East, Canada to the West and Svalbard in Norway to the North-East.
Greenland is usually divided into the following regions:
Don't be too concerned about the cities' formidable names. Most have more accessible (albeit now unofficial) Danish names as well, which will also be recognized.
Flights to Greenland will almost always go to one of the two following airports. From there local flights or boats will take you to your final destination.
Although maps with flat projections of the globe tend to make Greenland look the size of Africa, it is actually "only" about the size of Mexico. Despite being a little bigger than Mexico Greenland has the world's smallest population density.
It represents some 97% of the area of the Kingdom of Denmark, a territorial claim with roots in the 10th-century explorations of the Vikings, changing hands several times over the centuries due to developments in Europe. The local Inuit (also known as Kalaallit, but don't call them Eskimo; it's considered an insult) have closer cultural ties to the inhabitants of northern Canada (also Inuit) than to any of their European associates.
According to legend, the name was chosen to entice people to settle here rather than Iceland. Ironically, Greenland contains phenomenally more ice (about 84% of its immense surface area), and Iceland's climate – punctuated by geothermal hotspots – is generally more mild and hospitable to green plants. In fact, it is more likely that Greenland was named simply because its southern coasts (the first part of land sighted by the Vikings) appeared green and fertile during the Medieval Warm Period.
Be careful with maps of Greenland, as many Greenlandic names simply reference a particular geographical feature. Thus, a name like "Kangerlussuaq" is more common than you might otherwise expect, as it simply means "Big Fjord".
When visiting a city/village don't be afraid to ask for directions of shops, places to eat or somewhere to sleep, even if you think there might not be any. Most places (even Nuuk) are small enough for everyone to know where everything is, and therefore no one bothered to put up a sign. Don't be surprised to find a fully equipped supermarket inside a grey factory-like building somewhere in the middle of nowhere.
Danish and other Scandinavian citizens do not need a visa for Greenland, but your passport needs to be valid for at least three months after your visit.
Generally, if you need a visa for entering Denmark, you also need to apply for a special visa for entering Greenland. Visas for entering the Schengen-area (including Denmark) do not automatically apply for Greenland.
Visas are available from the Danish embassy or where you usually would apply for a Danish visa.
If you stay for more than three months you need to apply for a residence permit at the police station.
If you stay on the typical tourist paths you do not need any permissions, but any expeditions (including any trips to the national park, which by definition are expeditions) need a special permit from the Danish polar center. If travelling with an agency they will usually take care of the paperwork for you.
If you are entering or travelling through Thule Air Base, you need a permission from the Danish department of foreign affairs, since it is a US military area (doesn't apply for children u. 15, Danish police and military, US military or US diplomats). See Qaanaaq for details.
Air Iceland  operates a regular flight from Reykjavik to Kulusuk, Kangerlussuaq, and Nuuk; one to Ittoqqortoormiit, and another to Narsarsuaq. (Note that they use the Danish place names for some of these.) One popular day excursion is to fly from Reykjavik to Nanortalik, where traditional handicrafts are on sale, before returning to the comparative comforts of Iceland.
Scientific and technical personnel traveling from North America for research purposes typically fly into Kangerlussuaq aboard New York Air National Guard C-130s. Air Greenland also offers flights to Greenland from Baltimore/Washington International Airport.
If you are looking for the airport, the name of Greenland's airport service is Mittarfeqarfiit.
There is no ferry service from Europe or the rest of North America. However, there are cruise ships from both continents that visit Greenland.
There is no road or rail system. The easiest way to get around Greenland is by plane, particularly Air Greenland. In the summer, Arctic Umiaq Line  passenger ships provide service to destinations between Narsarsuaq and Uummannaq along the west coast.
The official Inuit language (Greenlandic, also known as Kalaallisut) is actually that of the more populated western coast. The eastern dialect is slightly different. Both are highly challenging languages to learn, as words are very long and often feature "swallowed" consonants. Try uteqqipugut or Ittoqqortoormiit on for size.
The good news is that almost all Greenlanders are bilingual Danish speakers, and many will even have a functional command of English. Greenlandic words may come in handy for travellers wanting to experience the "real Greenland", though.
Greenlandic is different enough from Inuktitut, the language of the Canadian Inuit who share similar historical roots to the Greenlanders, that the two peoples have difficulty understanding each other. However, attempts are being made to unify the Inuit language, and Greenlandic -- with its existing libraries of translated Shakespeare and Pushkin -- seems like the most natural option.
These are the names to look for, if you need to buy groceries:
Food in Greenland is generally not that different from American or continental European tastes. Restaurants carry typical European fare. Local food can be purchased at local markets in each town. Many Greenlandic restaurants combine traditional foods (locally-caught fish, shrimp and whales; also muskox and reindeer) with more familiar dishes. Expect to find whale meat at a Thai restaurant and caribou in a Chinese joint. Nuuk also has several burger joints and a couple of very high-end restaurants, most notably Nipisa, which specializes in (very expensive) local delicacies. Prices are high everywhere, but servings are generally large, especially with fries.
A local specialty is Greenlandic coffee. Its creation in some places is pure performance and it hits hard: it's coffee laced with liberal amounts of kahlua, whisky and Grand Marnier. One of the best places to buy is at the Sukhumvit Thai Restaurant, for about $22CAD.
Greenland is expensive. Nice hotels exist in all of the more visited areas (Hotel Hans Egede in Nuuk, Hotel Arctic -- with its igloo rooms -- and Hotel Hvide Falke in Ilulissat), but cheaper options exist. Try for the Seaman's Home hotel in Maniitsoq, Nuuk, Qaqortoq, Sisimiut and Aasiaat. Also check with the Nuuk Tourism office for its hostel program, where locals have rooms they will rent out for a third the price of the town's hotels. They usually speak Danish and Greelandic, along with very rudimentary English.
Crime, and ill will toward foreigners in general, is virtually unknown in Greenland. Even in the towns, there are no "rough areas." So long as the visitor uses basic common sense and etiquette, he or she should be fine.
During the northern summer, the days in Greenland are very long. Always make sure that you get as much sleep as you're used to, as sleep deprivation can lead to all manner of health problems.
During the summer, also watch out for the Nordic mosquitoes.
As mentioned above, the word "Eskimo" is not one the Inuit use to refer to themselves and is in fact considered insulting, as it refers to the local equivalent of "cavemen".