Basically, color lithography. Webster likes to say this about lithography:

"The art or process of putting designs or writing, with a greasy material, on stone, and of producing printed impressions therefrom. The process depends, in the main, upon the antipathy between grease and water, which prevents a printing ink containing oil from adhering to wetted parts of the stone not covered by the design."

Color lithography meant having to use a separate stone for every color. Pain in the ass. Here's just how much of a pain:

Between 1851 and 1853 in England, a massive publication was underway: Digby Wyatt's The Industrial Arts of the Nineteenth Century at the Great Exhibition. This book contained 160 illustrations printed by chromolithography, and each one used at least seven colors. According to the preface, 1,300 copies were printed, at a rate of about 18,000 impressions per week, for a total of 1,350,500 impressions in all. After each impression, the lithographic stone had to be thoroughly cleaned. 1,069 stones were required, weighing 25 tons altogether.

Courtney Lewis, the color printing historian (those exist?) said, "With 1,069 stones, the place must have looked like a dismantled cemetery. No wonder, as then practised, chromolithography waned." But the process stuck around longer than you might imagine - over the next forty years, chromolithography steadily outpaced its rival processes until, one day, poof it was replaced by photography. At the height of its popularity, and implemented correctly, the process was capable of incredible results. See http://www.octavo.com/marginalia/chromolitho.html for an example - it's really quite lovely, especially considering this was a mass-production, and created in the 1850s.

Chromolithography was fist made popular in the US by Louis Prang, who helped pioneer the process, and used it to print the first American textbooks, maps, color portraits, as well as America’s first Christmas cards.

George Audsley's 1883 book, The Art of Chromolithography, provides a thorough description of each step of the process, here summarized in plain English:

An artist first analyzed the original painting or drawing and then prepared a reference drawing on tracing paper, "not only giving the outlines of the object or composition, but also minute indications of the boundaries of all colours, lights, and shadows." This tracing was then transferred to a lithographic stone, and firmly affixed.

In some cases, there was so much detail in the original artwork that the copyer had to make his tracing from an enlarged photograph of the original. This enlarged version was then reduced by - get this - they got a piece of india rubber of uniform thickness, stretched it taut in an iron frame, then pressed the enlarged copy against it, then slowly released the india rubber and let it contract to its original size, hoping against hope that the proportions didn't go all wrong.   "The operator immediately commences to relax the india rubber evenly on all sides, carefully watching the manner in which the drawing contracts in its various parts. By skilful manipulation of the numerous screws he at last reduces the transfer to the required size, with all its angles and details perfectly true, as in the original drawing."   This seems insane, but it apparently worked.

Then the guy decided how many colors of ink would be needed. He prepared "a scale of colors," a kind of "paint-by-numbers" watercolor sketch showing which inks he needed, and in what order they should be used. When necessary, a skilled chromolithographer could obtain "several degrees of strength" from one color by using graduated lines, hatching, or other shading techniques. Most fine lithographs of the late 19th century used between ten and twenty-five colors.

A series of printing plates, or stones, were then made. Copies of the tracing were transferred to the necessary number of lithographic stones, one for each color. The artist used a special fatty black ink to carefully paint in the areas designated to receive each color of ink; he proceeded until each stone carried an ink-receptive image area for its particular color. Usually the lighter colors were printed first. Of course one had to be damn careful when aligning the paper between colors, and many books were printed with slight irregularities.

Chromolithography quickly became the dominant color process of the century. As the people doing it got better at it, rival processes like wood-engraving fell by the wayside, except for the cheapest kind of printing. There were of course plenty of cheap "chromos" to be had, but at its finest, the process had "a graphic quality and a freshness of colour," which, says Ruari McLean (who?), "modern dot-infested photographic printing processes have lost."

For many people, especially in late nineteenth-century America, chromolithography made color prints cheaper, and thus made it possible to own reproductions of famous works of art, for the first time. (And a million dormroom Starry Night posters were born.)

The process had its critics, who saw the process as a corporate attempt to supplant real art. The art critic Philip Gilbert Hamerton called "the employment of chromolithography to imitate the synthetic colour of painters... one of those pernicious mistakes by which well-meaning people do more harm than they imagine."   Lewis Mumford (oh, him) was even more direct, declaring that "the cheaper chromo-lithograph only increased the amount of futile work in the field, helping printers to flourish whilst it encouraged the original artist to starve."


thanks to:
http://www.octavo.com/marginalia/chromolitho.html
www.prang.com
http://rmc.library.cornell.edu/ornithology/exhibit/exhibit5.htm
Webster 1913