My scarves are sewn from one or two long pieces of material that are usually all cotton or a cotton blend, sometimes flannel. The ends are sewn together to create a circle, the fabric is turned inside and all the seams are hidden resulting in a pretty loop of fabric that can be worn many ways.
The typical scarf I make is about 58 inches round/long and 7-8 inches wide. This is my favorite size as I think it's the most versatile, it is long enough to be twice around your neck, like shown below. (This is one of my most popular scarves by the way.)
I also make smaller ones that are just 3-4 inches wide and about 30 inches long, call them necklaces if you will. These are great for smaller people, or just the ones that don't want so much scarf, but still want to show some team spirt. They are especially nice in warmer climates. You see that they can be folded or twisted to show more of one side or another.
Pretty much any two pieces of material can be sewn together, I think the contrast is really cool when I pick two different co-ordinating fabrics! I can also make the scarf with the same material on both sides, like this beautiful blue Boise Broncos one below.