This is simply two part resin with some tinting added to it. I mixed it and then poured it in a thin stream to roughly fill the engraved areas. Once everything was filled, I used a piece of scrap to wipe the excess resin off the surface (you'll clean up the areas between the letters more later in the process).
This resulted in the filled areas being slightly lower than the surrounding stone which is a good thing because the resin dries "smoother" or shinier that way.
I also used a butane torch (you'll find how to do this online) to remove bubbles from the surface of the resin. When it was 99% cured, I used a rag and some solvent to wipe clean the areas between the letters and other areas where there was resin still smeared on the surface.
Hope that helps. Feel free to ask if this wasn't as clear as it should be...