Trim your paper tube down to about 18 inches (you don't have to, but it makes it easier to handle).
Now you start taking the lights off the tree. Begin by placing the plug end inside the tube through the slit.
Next, you just start wrapping the string of lights around the tube, doesn't matter how it's spaced out, but should be taught against the tube. I'm starting at the bottom and wrapping up towards the top of the tube as I go along.
Once it reaches the top of the tube you just use your hand to push it down, so the strings are now all close together.
Repeat until you have gotten to the end of the string of lights. The nice thing about this method is that if you are taking down the tree by yourself (like I was) and your tree is up against a wall, it is easy to just place the tube on a branch on the back of the tree and walk around to the other side and pick it up (passing yourself the baton, so to speak).
When you get to the end of the string of lights, put another slit in the top end of the tube (just like you did for the bottom of the tube) and tuck the plug in.