You don't "stone" the table, you use a stone as a burr detector. A stone glided over a flat surface will detect the smallest raised metal and a little localized effort will bring the raised metal flush with the original surface. Theoretically stoning the table surface if done right causes it no wear but there's always a little. The more sensitive and skilled the stoning the less wear. I've seen Sip table still exhibiting their original scraping after 20 years of continuous use marked only by hundreds of tiny bull's eyes where the raised metal surrounding where a little piece of grit or a chip was driven into the table and silver streaks either side of a scratch was removed by skilled stone work.
It's not a perfect world. You clean and wipe, taking great care but one in a while something gets past you,.forever marking what should remain pristine. It happens and when it does you glide a stone over it, cursing whoever raised the blemish including yourself.
I've seen knuckleheads attack machine tool work clamping surfaces with files and for some reason nobody shot them, I don't know why. Monkey see monkey over-do, maybe. Some behavior merits a Darwinian award.
The preferred stone for this kind of work is a "slip stone" or "abrasive file". You don't want to use grandpa's old bench stone on a machine table. I prefer a fine hard India stone from Norton. Usually these are orange to cinnamon colored stones that come is a variety of shapes and sizes. I prefer a 1 x 1 x 6 square. These are aggressive when new - too sharp for burr detection and a little off geometry.
One of the stone's surfaces needs to be smoothed for table stoning - and only table stoning. Since the faces are seldom flat, I dress the concave side briefly on a DMT coarse diamond sharpening stone or 220 wet or dry just enough to dress it flat to slightly concave and blunt the surface abrasive. I do this under running water to control abrasive drift. WD-40 is nearly worthless as a preservative or lubricant but it is an excellent cleaner and stone oil. I foof a light film on the table, wipe it clean, foof again and glide the stone..
There are many tricks, trivia, and picky details relating to machine shop activities. The good part is, it only takes a few years to pick up enough of them to become a tiresome bore, a source of unasked-for advice to noobs who, wishing to know only the time, have to listen to you lecture on how to build a clock.