You'll want the hook to face out, if possible, unless you want to add a strip of protective fabric so that the hook doesn't rub on your skin.
Pin the front strip so that the crease of the hem (or overlock stitches) are matched up exactly with the front edge. You will be putting the fabric over the top of the hood and eye fixtures to hide them. Pin, then cut a diagonal line from that strip also, so that the two cut edges match up (same red dotted line above).
Unpin and sew the two cut edges together with a 1/4" seam allowance. Remember that the two pieces will be offset, as the collar piece has a ruffle overhang and the front does not. Follow the fold in the seam allowance when you get to the collar piece, so that the ruffle is hemmed. Re-pin, and it should look like this:Repeat the procedure for the bottom corner, leaving 1" of the chiffon overhanging the bottom hem of the cardigan. When you're satisfied with how the chiffon lies, stitch it on as close to the hems of the cardigan as possible. When you've finished, add another line of stitches 2" from the first.
The buttons they show on the Madison Cardigan are sparkly glass buttons, covered with the chiffon to mute the brightness. They're only decorative, so it's entirely your decision whether to leave them off or not.
To cover a button, cut a circle from the chiffon, stretch it tightly over the button and gather it at the back where the buttonhole or loop is located. Wrap thread around the bunched fabric to secure it and run a needle and thread through the center of the bunch for added strength.
Personally? I'd prefer to experiment with paints instead of buttons.
As an alternative to the Chiffon, you can use silk, polyester, lightweight leather, etc. I'd highly reccomend a strip of silk, but making it only 2" wide and leaving off the ruffle; simply stitch it onto the cardigan at both hems of the silk to secure. Using kimono-print poly silk (which is machine washable) and bamboo buttons would look great.
If you need to size up even further (but the armholes fit) sew a strip of fabric about the same color as the cardigan or chiffon to the hem and front of the cardigan. After you've extended the edge, continue as before, adjusting the width of the chiffon strips as needed to disguise this additional fabric.