We have an inexpensive digital camera that is a few years old. And I LOVE the light displays at Christmas time. SO I needed to figure out how to take quality pictures of the lights. If you want to know how I did it, I'll tell you:
Our camera has a scene setting. It is marked as SCN on a dial at the top of the camera. When the camera is set to scene, there is a sub-menu that you can scroll through on the screen. If you would like to take pictures of the lights at Christmas, choose "fireworks" from that sub-menu.
Now, when you take a picture on this setting, you will have to be REALLY patient. You click the button to take the picture and then the shutter stays open for a really long time to capture the picture. DON'T MOVE! Hold your camera as steady as you can until the picture is taken. You may think that something has gone wrong with your camera. It hasn't. Hold your arms still and keep them pointing at your object. After several long seconds, you will hear the camera take the picture and see the image on your screen.
The seconds it takes to take the picture seem like an eternity, but do not despair. Keep your arms as steady as you can and your camera pointed at the picture you want and you will be rewarded. This is the best way I have found to take pictures of especially low-light situations. And, as you can see, I get pretty good results with light displays. Give it a try!