How does Fluther program the links between a question to a list of appropriate, related topics?

First off, your question will be moved to “Meta” by a moderator because it is a question about Fluther itself. That’s the first major division on Fluther: General, Social and Meta.

As far as I know, the questions are then managed from the preexisting topic choices you chose after the details section. You can type in anything you like, but I believe only the auto-fill topics manage the question. These can be added to a user’s lists of interests. Hover over a red topic above and you’ll get stats. Fluther is no longer under development, so it’s doubtful that new topics are added.

You might do better to ask this question as a general development question as opposed to a Fluther question. i.e. “How can I program a simple task that creates the correlation of some text to some category/topic.” Just an example…you can do better.
Mentioning Fluther pushes you question to Meta, and it can languish there. We have some pretty good programmers here – given the right time and place you’ll likely get a great answer.

Typically, such a program will allow users to categorize the data themselves, by allowing users to create tags and apply them to their own (or on some sites, to others’) content. It can also scan the title or even body text for matches. It probably has a rating system that gives points for title (and maybe body) matches versus tag matches. The highest-scoring matches get chosen as related. It can be made more or less complicated and the values can be tuned to taste.