I chose to reverse applique this block. Don't be scared of reverse applique. It's not really harder than normal applique and your placement will be perfect. Another advantage of this method is that the seam allowance won't show through the light block as it would with traditional applique.
This being said, you are, of course welcome to use whichever applique method you choose. I've seen many blocks online done using either technique.
This is my method for reverse applique:
Trace or print the pattern from the book onto freezer paper and cut it out accurately on the seam line. Cut out the inside of the tears.
Cut a 6" square from each fabric you will be using. This will allow you extra fabric for trimming the block down later.
Iron the freezer paper to the center of the fabric that will be your "background", the darker fabric in this case, using a hot, dry iron. (The tears will be white.)
Cut out one of the tears leaving about 1/8" seam allowance all the way around. Cut only little holes in the other three tears for now. This will allow you more fabric for pinning/basting while you applique the first tear.
Clip vertically into the seam allowance about every 1/8", almost, but not quite, to the edge of the freezer paper. This will allow the fabric to form curves without pulling.
Layer the fabrics with the "tear fabric" - the white in this case - at the bottom and the background on top as shown in the photos.
Pin or baste the layers together, being careful not to baste too close to the edges of the tears.
TIP: I found that pinning through the freezer paper makes it pop off the fabric, so I would probably rather baste.
Using tiny whip stitches, applique around the edge of the tear, pushing the seam allowance under as you go with the tip of the needle. Use the edge of the freezer paper as your guide. Add extra clips or trim the seam allowance as needed.
I forgot to take a photo of this step. This diagram should clarify it somewhat, although they didn't seem to use whip stitches.
After completing the first tear, trim and clip the seam for the tear opposite it and applique. This is very helpful in getting your block to lay flat when you're done.
You may also want to re-iron the freezer paper to attach it to the fabric again because it does tend to come loose as you sew. You can do this several times before the freezer paper will stop sticking.
Applique the remaining two tears in the same manner.
Accurately trim the block to 5" by adding 1/4" to each side of the pattern still on the block.
Remove the freezer paper, press, and you have a brand new block!
(The photos are much clearer on Flickr, so if you want to see more detail, pop over there.)