To get this clean, Linda normally puts some old rags in the bottom of the sink, pours bleach on them, and goes to bed. The next morning she hopes that the bleach filled cloth was touching every inch of the sink bottom or she'll have a very dirty spot left.
Enviro Cloth and Cleaning Paste. It took a little elbow grease but we were able to remove most of the gunk. She found this much easier and more pleasant than the bleach option.