A möbius scarf is a continuous loop with a half-twist. That half twist makes it fit around the neck very nicely. I got the idea from a basic description for a knitted möbius scarf I found on the web.
Choose a reversible pattern stitch (i.e., one that looks the same from both sides). I used a moss stitch (work a single crochet and double crochet in the same stitch, skip next stitch).
The number of stitches in your foundation chain depends on your yarn, hook size and personal choice. Crochet your chain, drape it around your neck and hold the two ends together. Decide if it is too short, too long, or just right and adjust the number of stitches accordingly.
I crocheted a foundation chain of 180 stitches and worked a moss stitch in every other chain across.
Then I went back to the beginning of the first row and worked a moss stitch in the back of the skipped chains. You now have a circle. Slip stitch in the first stitch to close the möbius loop.
Now you have a twisted circle that appears to be 2 rows, but you have a continuous edge from the first stitch ('F') to the last stitch ('L'). You have just completed the first round.
Chain 1 (or number of chains for first stitch of your pattern stitch) and work next round.
The scarf is worked in rounds. Because of the half twist, one round results in stitches worked on both sides of the beginning chain. I found that I needed to reverse direction on each round to keep the scarf from curling. Keep working in rounds until the scarf is the width you like.