How far do you want to go back? I can not do a detailed explanation, because I am not a historian, but let's play a bit with the idea.
In the early days of digital images, you did not care about color accuracy.
Some years before you just had 16 colors on a VGA monitor, and just 4 before that. So you care too little about a color profile.
Here is a rough simulation of how "Test Drive" Game looked.
The original colors of this came was Magenta, Cian, White, and Black. So changing them to have a Ferrari red was a real accomplishment. (These images have actually more colors than the original version, it is just to get the idea.)
And how you could switch the palette.
Before digital desktop publishing, you had "analog" desktop publishing, and yes, you had some "systems" to keep a decent accuracy on your process.
The first one that comes to my mind, and it is still in use is a color bar.
Of course, they are now produced digitally, but they are to control the printing process analogically, where the operator sees the bars and adjust manually the amount of CMYK inks.
You also included patterns like this
which gave you information about how much ink you were pouring into the print, and see how much gain you had. That is on the press.
Going further back on the pre-press process, when you "screened" a photo, for example, a black and white image you had some charts to calculate what was the current black zone of the image, the white zone and based on that data, calculate the exposure time of the film.
On this image, we decide that the whitest zone I want is the one marked on the upper circle and the darkest part is the lower red circle. Now we decide that our muddle gray on the photo is the one marked on the green rectangle.
Then we see on the specifications of the screening film manufacturer which is the recommended time for exposing that image.
Something similar was for the CMYK color separations, where you filtered the image and consulted the manufacturer's charts to see the correct exposure time of each plate.
At the end, it was very dependant on the operator's skills.
We can track the history of printing process seeing examples of those decades. Let's use movie posters as a reference.
On the 1960s posters we can see that 4 process printing was not that popular. Combinations of black and white with flat color zones are common, so the color depended on what we now call spot color, or the direct color of the ink. Sometimes an ink is used just to "tint" the image, not to have an accurate representation.
It is on those years when companies like Pantone tries to have some forms of standardization of colors.
So in the 60's, it was more important to have a decent color representation than having an accurate color representation. A lot of technologies had to evolve. Photographic processes, ink manufacturing, printing process, paper.
And stealing Danielillo's answer about color proofs, there were several methods, to see a last preview of the color.
They were created using the real negatives before putting them into a press, the most popular were ColorMatch and Match Print, that used some dust pigments to simulate the inks. You also had roll tests, where you actually printed some pieces before a big project.