Here are some of the basics:
https://en.wikipedia.org/wiki/Halftone
The original artwork or photograph had to be projected through a cross-hatch of lines to make dots on the printing plate. Since the printing process could only make full ink or no ink, the etching of this pattern varied the size of the halftone dots to get graduated tones. For color, you needed at least cyan, magenta, and yellow printing plates, and almost always a fourth plate called a "key" was printed in black to emphasize the details and also make better blacks, because the color inks were not ideal and would produce typically a brownish black. So, this was referred to as "four color" printing, and still is. Today, programs like Photoshop can be used to create these color separations, which are called CMYK.