First I removed the hardware and wiped down each piece thoroughly. They were in great shape so I didn't need to do any sanding or degreasing or anything.
I painted the outside of one of them a light color, a really light gray that looks white in some lights. I also paint the face of the drawer the same color. Then I painted the inset area bright purple, marking off the areas where I didn't want the paint to bleed with FrogTape (I hadn't done that in the below pic yet).