The finished quilt size is 98" x 130". There are 12 x 16 blocks in the layout. Allowing for a 1" border, that gives a block size of 8" (finished), which matches up with the 8 7/8" squares it says to cut.
Personally, I would cut squares at least 9" and then trim them down to size.
To make the half square triangles, put two squares together. Draw a diagonal line from one to corner to the opposite one. Sew on either side of the line, 1/4" away. Cut along the line. You now have two half square triangles. Open each one up and trim to 8 1/5" size. Here is a good
illustration of the method.
You'll need to look at the picture and count up how many of each type of half square triangles you need:
1) White and light blue
2) White and medium blue
3) White and dark blue
4) Light blue and medium blue
5) Light blue and dark blue
6) Medium blue and dark blue
Sew a bunch of the half square triangles and then start laying them out to match the picture. Sew the blocks in one row together. Do another row. Sew the two rows together. Repeat until whole quilt is together.
Personally, I would sew about half of the needed half square triangles together and then assemble them into a partial quilt and then do a few more smaller batches to complete the quilt, as this would help reduce the chances of accidentally sewing too many of one color combination of half square triangles.
Once all the blocks are assembled into the quilt, add the border on all four sides.