So now that we understand the better application or type depends upon the position of the repair area lets go after the repair itself.
Clean the area out first using Acetone (Take all the precautions, gloves, eye wear, drop clothes etc) and thoroughly clean with depression and surrounding stone with acetone and allow it to fully evaporate before proceeding any further.
Fill the chip or scratch in thin layers allowing the glue to fully cure in between layers so that your chip or scratch is cured fully from the bottom to the top. In Fact overfill the hole so that you have a little too much in the cavity.
Now that the hole is slightly over-filled you have to shave the excess glue from the stone with a razor blade but how you hold the blade is critical to the finished repair. You must not try to cut the excess off even though that is what you might think would be fastest and best to do. You have to actually scrape the excess off slowly by shaving holding the bade at a 90 degree angle and alternate the shaving motion from different approaches so as to not pull the glue out of the cavity but instead to get the now hardened glue completely flat with the surface. If it pulls out or doesn’t turn out quite right you can add more glue and re-scrape the top later.
Depending upon the color of the stone, the clear super glue usually looks very good in color as it takes on the surrounding stone color and blends in very well. There are exceptions and limitations to this. Very dark stones may be better off with Pigmented epoxy to blend the color and big chips or deep scratches may be better off with pigmented epoxy as opposed to Cyanoacrylates.
Some scratches are better off being polished out as opposed to filled. It depends upon the individual stone and the depth of the scratch as well as the finish of the stone. Polished vs. Honed Vs leather-ed or what some people refer to as antiqued. This is not the only or even the best way for all scratches chip and cracks but it is the most popular and effective for most……….NOT ALL. Use this information at your own risk and consult a professional stone fabricator if you are not certain.