In addition to the excellent advice from the previous posters, I would only like to make a couple of comments. I do a good bit of this work, though less than I used to, since many of my artist clients now have you-know-what cameras.
I use two matched studio flashes with either a softbox on each, or large round reflectors. I measure carefully to set them at the same height as the center of the painting. An angle of about 45 degrees is good, but depends on the reflectivity of the art work. A more shallow angle from the plane of the art will increase the texture, showing the brushstrokes, while reducing reflections. A greater angle (lights nearer the camera axis) will reduce texture, and may increase reflection.
Acrylics and varnished oils will be more likely to have reflections. Watercolors are not usually a problem unless they are framed behind glass. In the case of highly reflective surfaces, the best solution is to put polarizing screens over the lights, both oriented in the same direction, and then a polarizing filter over the lens, turned so that the polarizing is at right angles to that of the screens. You can clearly see the effect through the lens.
I use an incident flash meter to determine exposure, and meter the center and all four corners of the art work to be sure the illumination is even. Don't forget to allow for the filter factor of the pola filter, if you use one.
I use a tripod with a pan head (a ball head will drive you insane) and geared post. Be sure that the camera is directly in front of the center of the art work. Level the camera with a pocket level, then raise or lower the post until it is centered on the painting.
If shooting 35mm, hang the painting horizontal, regardless of its normal orientation. You do not want to have to turn your camera horizontal; it's harder to level.
The best film I have found for art is Ektachrome EPN 100. It is neutral balanced, with no "enhanced" saturation of color or contrast, and is designed for reproduction of accurate colors, such as for copying artwork. In 35mm, I usually bracket one stop each way in half stop increments. With 4x5, I bracket a half stop over- and about 2/3 stop under-exposed.
I rarely shoot art with negative film, as the printing process adds another variable to the problem of matching the colors of the original. And the lab never has the original to use for reference.
Hope this helps.