This is not an easy question to answer: in fact, there is potentially a lifetime’s study in this. But I can point you to a place to start.
It is, at first, incredible to discover just how difficult it is to accurately photograph something that is perfectly flat and doesn’t move. Most of the training and advice given to photographers is irrelevant here. There’s no need to worry about composition, for example.
The problem anyone will encounter when trying to photograph a painting with a colour digital camera is that digital cameras don’t “see” like we do. The spectral response curves of an RGB sensor do not resemble the response of the human eye. Therefore, any colour photograph taken with such a camera is an approximation, at best.
The best-practice workflow is to photograph a colour checker in the exact same conditions that you photograph the artwork. Then generate a colour profile from the image, and then apply the profile to the image file. This will correct for any gross errors, but it won’t be perfect because of the spectral response differences. And, of course, you’ll need good lighting, with a very high CRI, that does not vary at all from shot to shot.
(And what does “perfect” mean, anyway? You and I don’t have the same eyes, and our colour sensitivity will differ. Two colours that look the same to you might look different to me. We’ll leave perfection to the philosophers.)
The colour checker passport is a good start, but something like the Digital Color Checker SG, which we use, will produce better results.
The camera matters too. It sometimes shocks photographers to realize that digital camera makers, by and large, pay very little attention to accurate colour. They’d rather have “pleasing” results for typical scenes because that’s what they think most photographers want, and they’re right. Also, they improve light sensitivity at the expense of colour accuracy.
The most effective improvement we’ve made to our colour management process was to buy a Hasselblad X2D, which has the most accurate colour reproduction of any digital camera we’ve used. You get what you pay for.
Finally, read this:
https://www.betterlight.com/downloads/whitePaper/wp_color_accurate_photo.pdf