The process is simple but tedious. Remove existing grout with grout removal tool or box knife and install new color grout.

What a beautiful tile! Rule of the tump - always match the grout to the tile. Specially with such a strong patterned tile, otherwise the grout also becomes a clashing pattern. I'd pick light grey to avoid pure white cleaning issues. I have these type of tiles in my patio, you will have to be seal them with penetrating sealer after installation, but other then that you will love them forever

It's a lovely tile! I'd go light-mid grey (basically like the picture!), if you go dark then it's pointless having the interesting hexagonal shape and the veins will look a bit odd stopping and starting, and if you go too light it will compete with the veins in the marble and look to busy.

My subway tiles are hand made Spanish tiles. I don't know what you mean by textured artisan tile?? I have used white grout. Our home is nearly six years old, and the grout is still white. I always rub a cloth over tiles if I have used the cook top. Keep it clean after cooking, and then it can't get dirty.