[microtherion]

The second part of this confused me as well, because the algorithm only detects the existence of the cycle, not its length. However, once you know a node in the cycle (which this algorithm will provide), you simply go around the cycle once more and you have the length.

[Spivak]

More specifically you stop moving the hare and send the tortoise around again until it meets the hare counting your steps along the way.