You will need:
A pair of sharp scissors
About a yard of a nice knit fabric
A good sewing machine with the appropriate needles that won't snag or pull the fabric
A box of pins
About an hour
Things to keep in mind:
-When buying your fabric, choose something that isn't scratchy or rough because this will be lying against your neck
-Buy fabric that is a cotton blend and can just be thrown in the wash to avoid high dry cleaning fees
-Select fabric that has a texture so that when you heat up inside of it, your heat will be trapped in the texture so that it can keep you doubly warm
-You do not have to limit yourself to what the fabric stores sell. You can create your own textiles with some various fabrics and create a patchwork style fabric.
Step 1: Measuring and Cutting
Since I wanted my Möbius scarf to be really wide, I cut my yard straight down the middle from the fold to the selvages. Now I have two 18 in wide sections folded in half. That means that my scarf will be about 8 and 3/8 inches wide when finished.
Now pin one of the selvage ends to the selvage end on the other section, right sides together.
Step 2: Sewing and More Pinning
The next thing you must do is sew along your newly pinned selvages. Be careful not to stretch out your material while sewing because you could ruin the way the fabric lays when you are wearing it.
Now, you will want to take your very long piece of fabric and make a tube by pinning (right sides together) the long edges. Again take this for sewing being careful not to stretch the fabric.
Step 3: Making of a Mobius
This is now the time that it becomes a Möbius. Take one of the ends and turn it. Now you have a twist in the middle.
Holding the two ends together, right sides out, sew around the inside of the opening leaving a small space so you can have a clean inside seam.
Now to close up the small hole that's left you can flip its edges inside and sew using a machine or you can be especially clever and sew inside as well. I'm not very clever so I just used the machine to sew the last little bit as an outside seam.