I think it might be easier to make today than eighty years ago! Rotary cutters and rulers and strip piecing could certainly be used to make it easier to make. There are really just two different "wedges" to the block that need to be made. It can also be paper pieced quite easily which is what I did to make my six inch block. It went together beautifully!
Click here to get the paper piecing templates.
I hand drew the block to get the exact proportions that Nancy Cabot drew. Though you can find many Spider Web blocks to make, I did not find any with seven rings and the varied strip widths that Nancy shows. Her placement of her fabric colors is also different. I made it exactly as she shows it.
Here are the two wedges of the block
and a shot of the back of the wedges.
I'm trying to show you how the seams will nest together if you follow the templates exactly and start each wedge at the correct end.
I removed the paper before sewing the wedges together so I could nest the seams against each other.
Sew four sections together as shown at the right and then sew the two halves together and you are done.