Sometimes one could realize that a painting reproduced in a photograph is not as beautiful as the real one.
Surely the photographic representation absolutely can not capture all the physical features that a painting can offer to the senses; anyway, let us see how it is possible to get a representation which is coherent to what we see from real.

In the publishing industry, the reproduction of a work of Art requires many efforts and much investment. There are companies that have made extensive research on colour and the methods of typographic copying, and that are specifically specialized in the Fine Arts area.

The instruments used in this field are also very expensive: high resolution and large format scanners, colorimetric probes, repro-photographic statives equipped with specific lighting, etcetera.

And yet, it is sufficient to know some simple artifices to succeed in photographically reproducing a painting without particular and expensive instruments.

A painting is substantially an image almost bi-dimensional; almost, because his surface sometimes is not perfectly smooth, since the brush stroke or the very same canvas confer to it volumetric characteristics that modulate polish and reflections. Obviously this consideration is not applicable to a print on smooth paper.

In my opinion, in case of artworks (either paintings and prints) of not excessive size, the best solution to reproduce them, in a cost-quality ratio, is the acquisition with a flatbed scanner; the scanner, at least up to a certain degree, permits also the perception of these surface characteristics  such as the roughness.
Obviously it is necessary that the size of the artwork stay within the format of the scanner. I remind you that the most common format, A4, has a surface of around 21 x 30 cm, while a more costly A3 has a surface which is double, or 30 x 42 cm, and a not economic A2 measures around 42 x 60 cm, and so on with the A1 and A0, that costs and measures suitable for a specialized laboratory.

Instead, if the artwork is too large for your scanner, then it is possible to use a photo-camera, but in this case some advices are necessary.

Tripod - Use always a tripod. Often one have the need to take a photo of the painting already hanged in the gallery, and most of the times there is no sufficient light and the photo comes out motion-blurred, therefore bring with you a tripod. You may prefer the use of a higher ISO sensibility, and in this case you will face a degradation of the quality and sometimes also of the colour.
If the pose time will be long, but shorter than two or three seconds, then it is better to adopt also a release cable or a remote control. Also the in-camera self-timer can be useful to avoid the shake when taking the picture.

Lens - Do not use wide-angle lens, which sometimes deform the straight lines or can cause sometimes blurring at the corners; it is better to use a medium-tele or a normal lens (medium focal), taking the picture from an appropriate distance.
The tele-photo lens, proportionally to their focal length, can make motion-blurred photos more easily, hence using it with a tripod is advisable.

Lighting -  If possible, it is necessary to photograph the artwork in a suitable ambient: the best light is the natural one, coming from a window, even if low; in that case it is always better to use a long exposure with tripod than to turn on a lamp. The ideal lighting is that of the sun filtered by white and diaphanous tents, that uniformly diffuse the light in the ambient.
For whom who are provided, it is possible to photograph the painting also with the use of a flash equipped with a diffusion filter, which lows its power spreading it; the filter is usually a hood or a disc of white and translucent material. Instead, it is not possible to use the flash without the diffusion filter, since it generates extreme glares on the painting.

Angulation and surface - If possible it is better to place the painting on a easel and move it in a place of the room where the light comes on the surface with a suitable angulation: it must be uniform and must not to create glares and reflections; a grazing angulation may possibly valorize the materiality of the painting.
It is highly inadvisable to photograph paintings with the glass, anyway in that case it may be necessary to move physically sideways so that not to appear in the reflection; successively there will be the need photo-retouching to correct the perspective deformation caused by that angulation.

Colour fidelity -  Using the sun light there will not be much problems.
With digital cameras it is always advisable to make the white balancing (see the next paragraph).
Instead, if you use films, these are mostly calibrated for sun light at noon, so in case of sunset or dawn the photos will tend to have warmer tones; in these cases you may use special correction filters, that exist also for artificial lights, available at specialized photo stores.

White balancing - Either if you take photos with natural or artificial light (neon, incandescence lamps, etcetera) it is good first of all to calibrate the white point of light.
To do that you will need a camera that permits it; the automatic balancing, especially with not professional cameras or in presence of artificial light, is not reliable, hence make the manual balancing.
The manual balancing is done, after having selected the relative option in the camera, by framing a white surface (a wall for example) or at least a neutral grey (that is without coloured hues: yellowish, rosy, etcetera) and then shooting, in this way the camera will take the next pictures with that point of neutral white.
If there are no white surfaces, search for a piece of candid paper and frame it under the light.
Besides the colours fidelity will depend also from the camera, in case it is digital, or from the used film.

Remembering these little artifices one will not get a photograph absolutely identical to the original, anyway it will surely be suitable in most of the cases.