Before cutting, sew a line around the bottom. This will prevent it from fraying while you cut and sew later on.
Cut around the top of your sewn line.
Set your machine to a wide, but tight zig-zag, and stitch all the way around the cut edge. Zig-Zag two parallel lines and cut between to make it one long strip.
Bleach out any unwanted stains, and you're good to go. Stitch On!
TIP: To make it more antique looking, use 3-4 tea bags in a bucket of hot water. Dip the scarf in, and rinse. Place in dryer to set the stain.