First I rinsed all of the feathers off with a spray nozzle, avoiding the rest of the shade as much as possible. And let me tell you... it reeks. It smelled so horrible, I could not believe it. I went to sleep that night with the smell still stuck in my nose. Once all of the feathers were wet I lathered up some shampoo on my hands and carefully ran my fingers over the feathers. I could see the dirt washing off. In sections, I repeated shampooing and rinsing. I kept my shade on the edge of the sink and rotated it until all of the feathers had bee shampooed. I gently squeezed the feathers with a wash cloth. Then I turned it upside down to dry. After and hour or two the feathers were dry, but still stuck together. I used a hairdryer to fluff the feathers. It was magical. The feathers suddenly came back to life, back to defying gravity! It's so fluffy!
Keep in mind, my lamp wasn't super expensive, and it was old. I was fully prepared for the worst. I definitely recommend taking some time to research if you want to clean a nicer lampshade. But for your everyday bedside lamp, this will probably do just fine!