Step 4: Cut back the primary flight feathers
Using a clean pair of sharp scissors, clip around 2/3 of the length of the first 10 or so feathers on the chickens wing. Take a look at the diagram below to see roughly how much of the feather you should be cutting off. You can also use the chickens secondary flight feathers (located in the same position on the wing as the primary flight feathers, just closer to the chicken's body) as a guide.
The idea is to cut off a significant amount of the feathers, while not making a cut so close to the chickens wing that you make them bleed. Chicken feathers have blood veins extending into them about an inch or so. If you cut below this point, the feather is completely dead, the chicken feels nothing, and the wings get clipped successfully.
If you cut above this point (closer to the chickens body/wing) the chicken will begin to bleed through the cut feather and your chicken will be in danger. If that occurs, apply pressure to the tip of the feather with a rag, and get your chicken to a veterinarian. Corn flour or starch applied to the cut feather cuticle can slow the bleeding and help the chicken clot. Additionally, grabbing the base of the feather with a pair of pliers and removing it completely from the chicken wing can also help the chicken clot. This process will hurt your chicken, but in a pinch, it may save its life.
Apparently the veins in the feather itself just don't clot very well.
If you cut the primary feathers carefully, there's no reason why you should ever cause your chickens to be in pain or to bleed during this process.