We went to Jo-Ann's and purchased black-out material. They sell it in 54" rolls by the yard for $6.99 a yard (on sale today for 40% off). Since each panel of the curtain is 58" wide, the 54" width is perfect. We wanted the black-out material to be slightly more narrow than the curtains so the white didn't peak out when hung. The black-out material is vinyl on one side and feels more like a fabric on the other. We put the vinyl side facing out to the window, not sure it really matters which way it is hung.
I cut the panel of grommets off from the rest of the curtain and ran a zigzag stitch to keep the material from fraying. I wasn't really careful or neat with this part since I knew it wouldn't show.