Regular white vinegar works pretty well, esp if you can let it set for 10-20 minutes, then work on it with a rough nylon scrubber.

Once you've cleaned it, I've read where you can use PASTE car wax to keep it clean longer, but I haven't tried it. I'm not sure this would be good on the bottom of a shower or bathtub, as it might create a slippery surface... you might want to try a small spot first.

Sue