BLURRY
To fix the blurriness, I followed what Gordon Brinkmann said, and changed the image texture from Linear to Closest. Since my tile was a pixel image, I wanted the pixels to scale correctly, and that is what does it.
TILE
I have a single, flat plane. No subdivision or loop-cuts needed. Just a blank, flat plane. Add the tile image and put the UV to fit your tile (mine is a square.)
In the Shader tab, using the nodes, I have a Texture Coordinate node, which I can set to UV to repeat a single image, then I use the Mapping node, connecting the Texture Coordinate > UV to the Mapping > Vector.
Playing with the scale repeats the UV texture you've used. You want to be in Render View to see it. Ta-Da!
