I happened upon two Ikea lamp bases at the thrift store for a dollar each (similar to the JANUARIline, but older and apparently no longer available on their website). I found two Ikea RIPEshades in the as-is section at the Seattle area Ikea store.
Voila! Some basic disassembly, some basic wiring, and reassembly, and I've got two reformed-trashy lamps. You could totally do the same thing with has-been lamps, some Ikea goodies, and a little bit of patience.
Step 1: Disassemble the trashed lamps.
Step 2: Disassemble the Ikea lamp
Pull up on the metal part that holds the light bulb. Snip off the wires, and set it aside for now.
Step 3: Remove the top of the Ikea lamp
Step 4: Combine the Ikea lamp with the found base
The upright part of the Ikea lamp should poke out of the top hole of the base, with the cord extending out of the top.
Step 5: Reassemble the top of the Ikea lamp
Step 6: Put on the shade
Step 7: Get a light bulb!
One, because we're all self-sufficient like that!
Put the light bulb in, plug in your new lamp, and enjoy!