Trying to find information about the inset seam online is a hard task to do for apparel. I am not even sure if any modern sewing books show how to make one. The reason for this might be the fact it is a moderately difficult seam to sew on a garment.
Technically an inset seam is a geometric style seam that typically comes to a point. It requires a pivot and turn method on the sewing machine. In addition, you need to clip the seam allowance at the apex/tip and press the seams well.
The point of an inset seam is delicate and takes on a lot of stress. I like to reinforce that area by hand. Not using too many stitches, so the point does not become bulky.
You can also sew it in three parts. I've seen quilters use this method. In quilting this is often called a Y-seam because three pieces of fabric are used to create the seam. The result is a seam that looks like the letter "Y". This video will best illustrate this method: Perfect Set-In Seams (Y-Seams).
Main Image: Photos taken of Vogue Pattern details and color adjusted and made into a collage.