I packed a 2-light kit, with 7" reflectors for the art, and an Octabank & Magnum reflector for the artist.
There are many pitfalls when photographing flat art, but the easiest one to botch it getting your exposure uneven. The solution is a lightmeter. Once you set your lights up, (at 45 degrees from the painting, sufficiently far back to wash the general area) start by metering the center of the painting for your base exposure. Then measure each corner and adjust the lights until you have less than 1/4 stop difference in all your readings (I prefer 1/10 stop). The following image is one of Katelyn's paintings with circles where I metered.

The next step was the artist at work; I set up the Octabank to the right of the camera and the magnum reflector to the left. You can see in this image the Octabank behind Katelyn, as well as the fill coming from the Magnum reflector behind my right shoulder.

There were many good shots, but I think this one clearly illustrates the lighting (as well as the acumen of the artist).

The last shot of the day was the headshot. I refuse to shoot "normal" corporate style headshots so tried to mimic the style of Katelyn's paintings in her headshot. Using the same basic lighting setup as the previous shot, only with the Octabank on my left and the Magnum on my right, I switched to a fast telephoto lens and used the modeling lights only to shoot. By mixing the modeling lights with the daylight coming through an open door, I was able to get a variety of pastel colors to play in the image. Later in Lightroom, I set temperature to 3200K to turn the daylight blue.

There is no single lesson to be learned here; just do your homework, have a plan for every part of the shoot, bring the right tools, don't be afraid to improvise.
Check out Katelyn's website http://www.katelynalain.com/ as well as her gallery http://www.skotiagallery.com/.