level the camera on all 3 axis', level the painting on all 3 axis', then measure the distance from the top right corner of the painting to the top right corner of the front standard (assuming you are using LF, 4X5 presumably). measure the distances from each of the corners, and they should be all the same. use a color checker chart (if you have one, but at least a grey card). use a slightly longish lens (say 210-240mm on 4x5), preferably a macro lens, due to the flat field. I've used an APO Rodagon on 4x5 before with EPY 64t 4X5, and it worked out totally fine. I shot a sheet with my 210(non macro), and the Rodagon looked much better IMO, much more accurate!
Do as all the others have recommended, and use lighting from both sides, and depending on the size, I prefer to use 4 lights minimum (on paintings smaller that 16x20), and at least 6-8 on larger ones. I don't do this for a living by a long shot, but I have some friends who paint regularly, and its a nice way to make some extra cash

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Many prefer to use continuous lighting (even the work clamp lights that you can get at Home Depot, and then diffuse them with some gels. I use up to 8 of them, and i point them at the opposite corner of the painting (so the light on the bottom right points at the top left corner of the painting, and the such. All the lights are at the same distance from the painting, and each is measured individually, one at a time.
Its a meticulous process, and usually not all that "fun", but it can be a rewarding experience to see someone's art entrusted in YOUR hands to reproduce it faithfully. Just put on some good music while you're doing it, and it won't get that boring

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If its possible, shoot a polaroid, or better yet, shoot a test sheet, process it(or get it processed), and then examine it for accuracy.
If no tungsten film is available, then I'd recommend the Fuji Astia, Provia, or preferably, the Kodak E100G, or ektachrome 64(EPR). of course, since these are all daylight balanced films, you will need to compensate accordingly with filtration.
-dan