If the slate isn't installed, there is no method. If it is installed, you need to use a damp cloth, not wet, and simply wipe it down. If a cleaner is needed because of a spill (soda etc.) you will almost certainly destroy the plaster of paris used to smooth the surface. The table will need resurfacing.
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You cannot make the slate for the pool table. It is cut and milled for the table, and then the table manufacturer fixes a wooden frame to the slate and fits it to the table frame. Then the holes are drilled to anchor it to the table.
There is no reason to find glue on the slate of a pool table. However, if someone other than a professional assembled it and glue is present, acetone is the most common solvent that will work for most glue. Scraping lightly with a razor blade may be required to finish the job.