I’ve always approached taking pictures of my paintings in the same way I used to take pictures of small products. Big advantage these days is colour balance. Digital cameras do this automatically but there are some colour cards that can be picked up from camera stores that can help. I just put a piece of white paper in the corner of the photo. The big problem is that the image will look different on every monitor. You just can’t guarantee colour.
As far as lighting goes, light the painting from each side at an angle. Not so much that it starts showing brush strokes but enough that it doesn’t reflect back into the camera. If you must, varnish the painting with a flat varnish. Sometimes I just can’t get rid of all the glare. The type of light that you use isn’t critical since the camera will compensate but it’s a good idea to use natural or full spectrum lights. Sunlight through a shear white curtained window works. Cameras are so good these days that even full spectrum fluorescents can give good results.
Now bring the image into an image editing application on your computer (Photoshop is the best but there are more out there). Adjust the levels and increase saturation slightly and don’t forget to sharpen slightly. If you are using the latest Photoshop the Vibrance adjustment is a mix of some of these but you still need to sharpen a little. Does the image look like the painting? That is the best you can do.
There are lots of good tutorials about this on YouTube.