How do I know when to switch to a finer grit when polishing marble?
I would suggest that to get a really smooth polish you will be using sand paper or polishing pads with grit numbers as fine as 3000 or more. The general advice is to switch to the next finer grit when you no longer see any remaining grooves or roughness left by the previous grit. 

You may need to experiment with looking at the area that you are polishing carefully to see how it is coming along. It will certainly be necessary to really clean up the area and remove all the dust and particulate that you have created. A bright light shining on the surface that you then look at from an oblique angle can help you to see the fine details. If you are using the dry polishing technique it may be useful to wet the surface to see how your work area compares to other parts of the marble that were previously polished.