My usual method is to wash the CD first in room temperature water, then pat dry. (get any dust off, and tiny specks of "scratch-ola" off too!)
I polish with tight oval motions from the rim to the center and back, not just perfectly straight back and forth, and proceed around the CD with the rubbing ovals until back at the start... etc. So it is a steady motion, not a jerky motion... like spirals, not zig-zags.