I inked the edges of all my circles with a small ink pad that I use for scrapbooking. It gives the circles a little more definition and helps tie all the colors together.
Next I took a piece of thin wood that was the length of my curtain rod and hot glued the cardboard circles to it. I offset mine to make it look more fun. To hang it, I just tied a piece of string around each end of the wood (but hidden behind one of the circles) and then tied it to the curtain rod. Easy peasy.
Here's the before and after!