I apologize if everybody knows this, but where can I find a description of the algorithm that is used to update the ratings following the result of a game? Thanks.

There is a section on ratings at Ed Collin's (inofficial?) littlegolem FAQ. It's the fifth question after the list of games with pictures.

What the FAQ doesn't seem to mention is that these ratings are an implementation of the Elo rating system (which is used virtually everywhere).