I started by using a 120 grit sanding sponge, which worked really well, even molding itself into the small grooves. Then I used steel wool, then sanded again the spots that were still heavily tarnished or still too shiny.
Then, using the same Valspar blue spray paint I used on the wooden nightstands, I gave the lamps two coats, allowing them to dry over night between coats.
I purchased two shades at the same Hotel Liquidators in Dayton (Ohio) - for $2.79 each, and I have a custom look for my bedroom that was super inexpensive!