How to take photos at night with Nikon D3100?

I just got a Nikon D3100 so I'm not very familiar with it. I'm trying to take pictures of these icicles outside my window and the moon is at a perfect place where it shines through perfectly. How do I capture this? I don't want a flash because I want to capture the natural light, and when I play around with the settings I can't seem to change the shutter speed so that the photo isn't shaky/blurry. Any suggestions?

Yes A tripod is key to sharp lowlight shots, i use the £18 "hama star 63" tripod. Its dirt cheap and works well, its lightweight and starts small and extends greatly but its not smooth super smooth. I use it for long exposures, for your image I say stick your camera in the "S" setting for shutter speed, twist the little rotate thing near the screen not the one on the top near the flasb and it will make the speed faster or slower, choose about 2 secs, if its not bright enough go higher, but the longer the speed the more blur and grain it produces, so use a tripod, or put the Shutter speed on 1/15 or 1/25 and set the ISo to 800, if its to dark make the shutter speed a little longer such as 1/5 etc. Hope I helped, please answer my d3100 question thanks

Buy a tripod and use a timer so you won't capture the shake when you press the shutter button.

Or just crank up the ISO and see where that takes you.

You are discovering that the next major accessory (besides little things like card, case, and extra battery) to buy is a good tripod.

Ahem! I said a GOOD tripod.