You adjust the images in software on the computer.
The most classic problem is "white balance". Most objects don't emit their own light... they reflect the light from other sources. If those "sources" have a tint to them (and they do -- even if you think they don't) then that puts a color cast onto the subjects in your photos. Incandescent light tends to create a yellow/orange cast. Florescent lights might create a green cast. etc.
If you want "exact" colors, you do two different things:
1) Take an image of a neutral gray card (this isn't just any "gray" object). The particular gray is designed to be a perfectly neutral gray and the camera and computer software know it. Colors in an 8-bit system are represented in tonality from 0 to 255 where 0 is black and 255 is the brightest level of that color possible. 0 red, 0 green, and 0 blue create black. 255 red, 255 green, and 255 blue create white. If you blend some amount of red green and blue and they're nearly equal you get a gray... but that gray may have some color cast. For example 100 red, 100 green, and 110 blue would be a gray that has a bluish tint to it. But if you blend red, green, and blue and they are exactly equal then you get a perfect "neutral" gray.
The idea behind the gray card is that if you take a photo of it and the computer records those pixels as, say, 110 red, 105 green, and 95 blue then the computer will realize that you have got an red/orange tint created by a "warm" light source. The computer then knows that it can boost the blue and decrease the red/green just fractionally to correct the color cast (and it does this to every pixel in the image... not just the gray parts.)
That creates colors which will be extremely close to correct... but not perfect. It also assumes that you aren't over or under-exposing your images, but that's a different problem.
2) You can also use a color checker. This is a card that, in addition to having a row of neutral grays, also has a row of RGB color tiles as well as rows filled with colors commonly found in nature (skin tones, blue skies, leaves, etc.) The specific RGB balance of the colors are also printed on a sheet that comes with the card. This allows you to snap a photo of the card taken in the same light where you'll be shooting. You can then check each color to determine if the camera has faithfully represented that color and correct the color if it's wrong. Those corrects can then be applied to all the other images you shoot (as long as they were shot in the same lighting conditions.)
In general, you really only need to white balance using a gray card and you'll tend to get accurate color. It's usually not necessary to ALSO use a color checker. When color checkers are used, usually it's because the photographer is doing product photography where accurate color is critical to the work.
