Natural Light
The best way to photograph flat artwork is to use natural light. If possible, bring the piece outside and find an open but slightly shady area. The shade helps protects the artwork from sun damage or curling. Place a white or black poster board on the ground near where the shade ends, as a background, then place the art on top of the poster board. If the art cannot come outside, it is still best to use natural light from a nearby window if you can, or light from a room where the art is hanging.
Taking the Shot
Before you take the shot, compose it so the outside lines are lined up straight in the frame. Do not use a wide angle lens, as it will distort the sides of the art. Instead, aim the camera straight down on the piece, and fill as much of the frame with the art as possible. Use a fast shutter speed. Also, bracket the exposures. Bracketing is when you take one shot regularly, then one overexposed shot and one underexposed shot, so you take three photos of each piece. To overexpose or underexpose the shot, adjust your aperture one f-stop up or down from where it currently is. Some cameras also have built in over- or underexposure settings. You might actually like some of the over- or underexposed shots better!
Reflection
Reflection might be an issue you run into when you shoot flat art, especially if the art has a glossy or laminated finish, or if you use a piece of glass on top of the art to flatten it for the photo. If this is the case, move the camera slightly until you get a shot without a reflection bouncing back. Or, get a piece of black foam core board and cut a hole large enough for you to shoot through. Stick your lens through the hole and shoot away. The foam core board will help absorb any reflection to help keep it out of your photo. If you need to use a flash because you are indoors, it is best to use an external flash, and position it on the side rather than straight at the art to help avoid reflections in the shot. Finally, use your favorite post-production tool(i.e. Photoshop) to add a bit of color warmth into the final shot if needed.