First, cut the background fabric. Measure your diamonds as shown.
To get the "A" measurement, simply lay two diamonds next to each other as they would look once stitched. Measure point to point and add about 3". It doesn't need to be super precise, but you definitely want it too big rather than too small. You can always trim. Cut one square using measurement "A" as the side length. Subcut this piece as shown, making (4) right triangles. This will likely be a large piece of fabric. Use a yard stick to mark the lines before cutting. It's critical that the 90 degree angle of each triangle is a perfect as possible. After cutting remeasure with a large square ruler and trim slightly if necessary.
For measurement "B", simply measure the side of a diamond and add about 2". Cut four squares using measurement "B" as the side length.
Next, start by sewing the diamonds into pairs. Refer to the picture below. We'll be using this same diagram throughout the tutorial for the order of stitching. Sew 1+2, 3+4, 5+6, & 7+8.
Mark each diamond with a removable fabric marker as shown. Mark a 1/4" line on wrong side of fabric along both sides of the wide angle on the diamond. Begin stitching at the intersection of these two lines. Pin two diamonds together, pinning where each border meets to ensure seams will match once completed. End the seam at the bottom of the diamond. Backstitch well on both ends. Press all seams open. Repeat with all diamond pairs. (All inside angles of star will be stitched in this fashion).
Next stitch the triangle background pieces to the diamond pairs (9, 10, 11, & 12 on picture above). Mark 1/4" lines on inside right angle of triangle (Example done using a square. Instructions are the same for either the side triangles or the corner squares).
Match intersection point on background piece with the point where stitching stops on diamond section.
Stitch across length of diamond. Stop stitching at marked intersections (where stitching began on diamond section).
Repeat with other side of diamond section.
Press seams open.
When stitching the triangles. Trim triangle points even with diamond edges.
Stitch diamond pair 1,2 to triangle 9; 3,4 to triangle 10; 5,6 to triangle 11; 7,8 to triangle 12.
Stitch pieced sections 1,2,9 to 3,4,10; 5,6,11 to 7,8,12.
Stitch square 13 to first pieced section, Stitch square 14 to second pieced section,
Stitch halves together. When joining the halves of the star, match and pin the center point first. Stitch with a basting stitch along only the center few inches (between the arrow points). If everything matches up, then pin the remaining length of the seam and stitch. If the center point doesn't match, unpick basting stitches and retry. Matching the center points is critical to the overall appearance of the quilt.
Stitch squares 15 and 16 to finish quilt top. Press all seams well. Trim edges to square quilt. Add borders if desired and finish quilt.