Ideally it should be decided by an editor, but that costs time and money. For something more automated, Hacker News already ranks comment threads by some measure of quality so the good stuff ends up on top and the obnoxious/otiose one-liners drop to the bottom.
HN lacks an API, but a decent web scraper (like BeautifulSoup) should be able to walk the DOM and grab the top threads.
Depending on space restrictions in the print edition, this could comprise:
* All comment threads with a score above some threshold;