Take one of the scarf's ends, and slide up an Anneau Infinity scarf ring (here a lacquered Anneau Infinity in ivoire). Don't slide it too far up, but keep it near the corners, where there is the least bulk of fabric.
Take the other end, and pinch the fabric as shown:
Then feed the pinched fabric through the ring, coming from below:
Next, pull out the first corner (where you slid the ring up) while holding onto the ring, as well as the loop you created in the previous step.