Hold the loom with one pair-of-pairs vertically in front of you.
Take hold of the bottom two strands (C & D), and move them both one space to the right (anti-clockwise). The right-hand strand will temporarily be sharing a slot with another strand.
Take hold of the top two strands (A & B) and move them both one space to the left (also anti-clockwise). Slot the right-hand strand (B) into place, but bring the left-hand strand (A) down to fill the vacant space at the bottom of the loom.
Lift the bottom-right strand (D) out of the shared slot and move it to the vacant slot at the top of the loom.
Turn the whole loom a one-eighth turn to the left (anti-clockwise), and repeat the whole thing again.
Keep this up until you run out of either patience or wool.
By popular demand (well, one comment, one PM and a phone-call), I have added a video of the weaving action: