He coated the rock in “a special epoxy” to prevent it from crumbling during slicing. Then, he washed the thin sections in a special dye that stained the DNA of the microbial cells.
What does that mean—I thought DNA was smaller that the wavelength of visible light? I guess it’s some larger molecule that binds to the DNA to make it more visible, but if that’s the case, “tagging” seems like a more appropriate term than “staining”.
The dye they used is called SYBR Green I. It's a molecule that binds to DNA and only fluoresces at a specific wavelength, but it only fluoresces once it's bound to DNA and exposed to a certain wavelength of light. You can observe the presence of bound molecules using spectroscopy which indicates whether or not DNA is present.
There are other fluorescent dyes, eg BigDye, which are used for genetic sequencing. You won't see anything with the naked eye, but an automatic sequencer can detect them.
tl;dr: "DNA staining" means they use something that reacts with DNA to indicate its presence. So if you paint the rock and it turns purple, you know where to look for DNA.
A single dna molecule is too small to see with the naked eye, but a few million dna molecules released from a few million microbes is easy to see IRL. In my bio lab days we did an experiment to isolate the dna molecules from a scoop of microbes, and at the end you wind up with a clump of dna molecules that together are about the size of an eraser head.
And yeah as the other person said, the term "staining" is the official term used for what you're calling "tagging"
It’s usually used for something that changes the superficial appearance of a thing without changing or obsuring its structure—and in this context it seems to mean making the DNA more detectable (by whatever means). I’m not picturing how this “dye” could do both those things at once on that scale.