The process was a very simple. I created a new metal frame out of a coat hanger, then wrapped a lampshade in plastic before winding the yarn around the shade. Finally, I covered the yarn with a simple modge podge solution to insure that it holds its shape.
As always, the best part of the diy is the cost. This cost me absolutely nothing as I used things I already have.
The idea came from here: http://cdn.homedit.com/an-original-yarn-lampshade-can-make/ They have a tutorial on creating a yarn lamp shade. All that's left for this project is to create a solution for the actual lamp.
Not one of my three cats has touched this and I found a lamp at the Salvation Army for $3 that fits the shad really well. So I'll upload a picture of that soon. It looks great!