What you see here is a USB Camera sitting in a coffee cup, pointing down at a blank sheet of paper. The cord is not actually in the way, it's above the paper.
Draw a small X on the paper where the code is supposed to go.

The coffee cup is resting on a book because that particular model of webcam does not have auto focus and needs a little extra height.

The blank piece of paper gives a plain white background.

When you slide the code card under the camera, it doesn't take a couple seconds to adjust the light, which results in faster scanning.
This is the best method I know for scanning the codes.