There are many trips to Greenland by boat or cruise that also visit Canadian Arctic or Iceland. You can also fly into Greenland (variosu places such as Kangerlussuaq) and explore the coast. The cruise ship options have ended for thsi year as most only run until September. You can do dogsleddign and see the northern lights in winter though. Some companies are Greenland Expert and Tasermiut and Topas Travel.

I highly recommend a little town called Ilulissat on the west coast of Greenland. Next to the town there is a spectacular icefjord bringing high numbers of massive icebergs into the sea. Ilulissat is north of polar circle, so the sun shines all night long at midsummer and there is a great chance to see northern lights (Aurora borealis) especially on wintertime. The town is very colourfull and friendly. It has about 4 600 inhabitants and even more (around 5000) beautiful sledge dogs. Dog sledging is possible only in the winter. You can get more info about Ilulissat and how to get there at www.worldofgreenland.com/

I agree with the other answers. You can also see what posibilities there is if you want to explore Greenland. www.airgreenland.com is a site where you can book hotels, flights, dogslegding etc. Maybe I'll see you in Greenland. :)

It also might be a good idea to fly there yourself and then look for day trip or overnight trip tours organised at your hotel once you are there.