In reply to 'Hilda':
Only visited southern Greenland, so these comments should be taken in that context.
Problem number one is not fitness, but the blackfly!! You'll definitely want a midge hood, and if you get the material, make a massive one that ties at your waist - that way you can eat outside!!!
Make sure you've got good sturdy boots (to a degree, this depends on where you go). Expect new boots to come back looking 5-10 years older!! When not amongst "meadows", you'll be in abrasive rocky terrain. Gullies and scree slopes can be particular "nightmares". Personally, I found poles useful, particularly with heavy weights. Oh, and yeah, watch out for the dwarf willow - it often hides big holes and crevases as it grows horizontally along the ground.
Avoid any peaks that look particularly spikey - typically this is poor weak rock and you'll be in for a mare of a time.
Essentially, you're operating in a remote alpine environment - its just that scree has not been compacted or stablized by the passage of many feet.
Great place and an amazing adventure - which is why I'm heading back there again this year!!
If you want more info, I'll email you links to our expedition reports?
ps.
I can strongly recommend "catching" icebergs - the ice from them goes great (with a snap crackle and pop) with whiskey!!!