The techniques used to photograph a work of art will of course vary with the nature of the particular exhibit, its location and the available light. The following comments are for this reason general in nature.
In the case of a painting hanging on a wall, a photographer's first thought should probably be to turn off the camera's flash. In most circumstances, the use of flash is more likely to ruin an image rather than improve it. Reflections from the surface of the painting will produce bright, over-exposed patches where all detail is lost. Light levels may be low, so without flash or supplementary lighting wide apertures and long exposure times may be required. This, in turn, leads to a requirement for a steady hand or the use of a tripod, shutter release cable etc.
It is also important to position the camera squarely in front of a painting. Unless the camera is positioned correctly, the rectangular painting may appear to be distorted. If a distorted image is cropped part of the painting may be lost or apparent curvature of the frame or edge of the artwork may become more noticeable.
Colour control is a key issue. Photographic lights should reveal accurate colours but available light or cheap work lights (such as halogen or tungsten sources) will lead to a distinct colour cast. This may be corrected in Photoshop but an accurate representation of the original work of art may still prove difficult to achieve.
Positioning the camera so that the angle of view is square (ie perpendicular to the plane of a painting) is critical. Unless the camera lens is correctly aligned, a distorted image will be obtained. This can be difficult to correct at a later stage. For the best results, set up the camera on a tripod and make suitable measurements relative to the centre of the artwork. If necessary, mark a perpendicular on the floor below the centre of the painting. Also measure the height above the ground of the centre of the painting and set the height of the centre of the lens above the ground to be precisely the same.
Ensure that the lighting of the painting is even and free of reflections and highlights. Diffuse natural light can be a good option. It does not matter whether the intensity is low because a low shutter speed can be used provided the camera is supported on a stable tripod and a shutter release cable is used.