Here's a non-mathy way:
You would need some translucent plastic, like cellophane, for the bombs. The grey is just all of the covered grid cells, and you reveal a cell by removing its cover. On the left you see what it looks like beneath the covers: a bunch of 3x3 cellophane squares with dots in the middles. The dots are bomb squares, and the surrounding red squares are what you use to determine how many bombs are in the proximity of a chosen cell. The darker the color, the more bombs there are.
You can randomize it by cutting each column of the board into its own strip, glue on the bombs for each strip, and then glue the strips back together onto a new board while it faces away from you.