I often see people looking for tips for shooting photos of artwork. Here are a few ideas.
Have the painting placed vertically on a wall (not leaning against something or inclined on an easel). Check it with a bubble level. I've painted the wall I shoot against a dark matte color so it doesn't reflect into the lens.
Make sure camera is placed on a sturdy tripod and use a shoe-mounted bubble level to make sure the camera is also level.
My favorite lens for shooting artwork is my 85mm f/1.8. It's very sharp and doesn't distort the edges of the work. I shoot at f/8, ISO 100.
Use hot lights at 45 degree angles to the artwork. You can see if you are getting specular highlights off the artwork. Flag off light if necessary. Make sure the light covers the artwork evenly.
Use a cable release and mirror lock-up to minimize camera shake.
Use a gray card and something to use as a white and black point to the side of the artwork to make sure your exposure is correct. Shoot RAW and adjust color and exposure in post-processing.
Adjust shutter speed for available light.