You can use any scarf shaped scrap of fabric that is the same on both sides.
You can use any yarn.
One of my scarves is listed in my etsy shop. Scribble Scarf
Step 1: Choosing Your Materials.
Another consideration is using yarn that's already in an impossible state of entanglement. It's satisfying to find a use for it besides tying up tomato plants.
Step 2: Let the Doodling Begin!!
In this step you decide on a pattern to repeat for your doodling, like circles, squiggles or straight lines. Now repeat it over and over by sewing the yarn onto the body of the scarf. DON'T PULL THE YARN WHILE YOU SEW....unless you want to. If you pull the yarn while sewing it will scrunch up the fabric. That might be an interesting design, too, but I don't want you to be frustrated if it isn't what you want.
You shouldn't have to worry about fraying edges because all the doodling with yarn acts to bind the edges.
If you have a fancy sewing machine you could sew the yarn on with a gourmet stitch and bright, contrasting thread, then appreciate the stitch on the other side.
Please don't worry about perfect replicas of your doodling. The doodling is fun because it doesn't have to be perfect. You can keep a theme, like circles, but all the circles are different.
Step 3: Repeat Theme on Each Side.
Alternating sewing your design between each side of the scarf will balance the doodling so each side is equally designed.....unless you don't want it that way. Maybe you only want the doodling on one side. It's up to you.
Step 4: Do Step #3 on the Other End of the Scarf.
Step 5: Keep Repeating Steps #2, #3 and #4...
Step 6: You're Done...
Step 7: How to Care for Wool
To prevent moth damage you can shake wool from time to time. You can put it in the freezer over night. You can iron it.
Never machine wash it and dry it unless you want to felt it.