Good advice about mountaineering and climbing
If you've decided on a climbing adventure in Greenland, you first have to find an area and time of year. Ideally, you'll have enough time to explore an area fully - hike in the region for a few days and find the fells and lines you wish to climb. See if it matches what you'd imagined it was like when poring over maps and photos in the darkness of winter.
High summer is best
Generally speaking, June, July and August are good months for climbing. There's plenty of daylight - in fact it's light round the clock - and boat transport is possible in most areas. The local tourist office is the best source of information about the exact area you're interested in. Please be aware that it's often difficult for local operators to say anything precise in terms of time and place - a lot, if not everything, depends on wind, weather and ice conditions. You'll understand this when you come to Greenland, and in fact you'll begin to enjoy the fact that not everything can be planned in advance. It's all part of the experience.
Clothes in fleece and wool
The summers in Greenland are mild - sometimes warm - and mostly pleasant. You don't need winter equipment, just standard alpine equipment. A good outer layer (Goretex or similar), fleece jackets and woollen underclothes, but a down jacket isn't necessary. A down vest can be comfortable during the evenings at the camp. Mosquito repellent is good to have (there can be a lot of mosquitoes in low-lying areas).
Equipment and food
Use a good, stable, quality tent. Use a stove that's efficient - for example an MSR Dragonfly or similar (you can buy White Gas (= heptane)/paraffin/kerosene and spirit from the local "Polar Oil"). At some places it's possible to buy freeze-dried meals, but it's probably cheaper to bring these with you from home. All other food, basic foodstuffs (pasta, rice, potatoes, chocolate, coffee, tea, etc.) can be bought locally.
Your sleeping bag doesn't have to be particularly warm - down to minus 5 degrees C is sufficient.
An ice pick is important
Climbing gear - in this case it's really a question of personal priorities, but the majority of climbing adventures are "alpine" - relatively long stretches featuring a mix of ice, snow and rocks. Therefore you have to think about climbing as light as possible and with equipment that's as versatile as possible. An ice pick and glacier equipment are very often necessary. A light, long rope, a light alpine harness and a selection of anchoring equipment that's versatile and not too heavy. Lots of slings and a couple of old-fashioned bolts are useful for long stretches of rappelling.
Draw on the experience of others
The above is very general advice - local tourist offices have a great deal of knowledge, but not always personal climbing experience. Try to find someone who has climbed at - or close to - the location to which you're heading. As you well know, the majority of climbers are more than happy to share their experiences with you.