A YouTube video of this is available here: http://youtu.be/n6FNQpUm-Ys
Step 1: You Need:
Thread (no needle necessary)
Step 2: Cut Sock
You also need to cut the other end. I recommend cutting about 1/2 inch into the "band" of the sock for the bottom of the cap.
Step 3: Cut Thread & Pinch End
Pinch the "top" end of the cap into gathers. Wrap the thread around the gather very tightly and tie off. Cut the thread very close to the knot.
Step 4: Create Pom-pom
Another option for a pom-pom-less cap: do Steps 1-3 with the sock turned inside out. Tie off gather as close as possible to the end. When tied off, turn sock right-side out. This will look more like the purple ski cap pictured.