Plastic beads in your choice of color. Mixes can be found in the crafts sections of large stores, and a larger selection of single-color bags is available at craft stores like Michaels. For this project, I ended up using roughly the equivalent of two bags of beads: half a bag of the black ones and one and a half bags of the clear red ones (I ended up having to get an extra bag of the latter).
Large pizza pan (mine is 16" in diameter). It's important for the pan to be large, because it's difficult to introduce a lot of curvature to the lampshade, and you still want it to cover at least most of the height of your light bulb. Especially if you intend to use a CFL bulb. The pan does not absolutely have to be round, but it really needs to be both wide and long.
Large stainless steel bowl. Metal is ideal in this case as it won't be harmed by contact with hot plastic, the plastic won't stick, and you won't chip, crack, or break it. You really don't want to use a plastic bowl for this, but ceramic or glass might work.
Aluminum foil. I didn't have the wider kind and regretted it, as it's difficult to overlap it without leaving gaps between layers for melted plastic to seep into and trap foil inside. Consider getting some for this purpose, if you don't already have any around the house.
A metal jar lid, like from pickles. It's going to help you create a hole in the lampshade. Make sure it's the right size to fit the mounting hardware of your lamp. Mine was a mason-jar style ring.
Non-stick cooking spray. It's optional, but I used some and didn't regret it.
Step 1: Arrange
If you aren't using a round pan with raised edges, consider creating a raised circular lip with the aluminum foil. Technically, you aren't aiming to make the plastic so runny that it will spill on the bottom of your oven and ignite on the heating elements, producing a lot of foul-smelling and probably toxic smoke, but it might be good to be on the safe side.
If you aren't using foil that's wide enough to cover your whole pan without layering, try to make sure the layers are as flush as possible.
Spray with non-stick spray when done.
Place your jar lid in the middle. Arrange the beads around it. It doesn't matter if they are all laying flat (like in my picture), but it won't hurt anything. Place them as close to each other as possible. Preheat the oven to 350F while you are doing this.
Open the kitchen window. Clear pets and children out of the way. These beads are going to smell a lot as they melt, and I'm guessing breathing in the fumes is not great for your health. You will need to check these every 5 minutes or so, but otherwise, stay out of the kitchen as much as possible. My beads took about 20 minutes to melt to my satisfaction, and I had to turn the pan about half way through the cooking time, because they seemed to be melting more readily on one side than the other. I was checking on the progress more often toward the end, as I didn't want them to overflow the rather shallow lip of the pan.
Step 2: Drape
Make sure your hands are protected with oven mitts, or at least securely wrapped in dish towels.
Pull out the pan from the oven. Lift the foil containing your plastic puddle, and flip it over on top of your bowl (which you should have prepared and waiting). Make sure the lid marking the hole is in the center of the bowl. Hold it there with one hand as you press down the foil-covered melted plastic down onto the bowl. When everything is mostly in place, you can let go and use both hands. Don't press too hard however: keep in mind that as the previously flat plastic pancake is being draped around a curved surface, the edges will gather into folds. You don't want to crimp those too tightly and trap aluminum foil inside.
When you are done here, walk away and let it cool. Or, if you are impatient, pick the whole thing up and run it under cold water. Just don't take the plastic off the bowl unit it's cool, or you could mess up the shape.
Step 3: Peel, Pop, and Mount
Take it off the bowl (it should come right off without giving you any trouble). Pop out the pickle lid. Mine took a gentle tap with a hammer.
Assemble the lamp and admire your creation!