Selected answers from the Dumb SEO Questions Facebook & G+ community.
Michael Martinez: Those suggestions are drawn from Google`s query logs. They probably use one or more machine learning algorithms to normalize the terms (sort of looking for synonyms) to figure out which queries are related.
There isn`t much a website can do to benefit from those suggestions. A few esoteric brand-related strategies for stimulating similar queries might work.
Shao Chieh Lo: Michael Martinez thank you a much, can you talk about the esoteric strategy a little bit more 😀
Michael Martinez: Shao Chieh Lo If you have a brand name "googly poogly" that people search for, give them a reason to search for "what to do with googly poogly", "how googly poogly works", etc. in sufficient volume that the search engine will show them as related searches.
What most people do is mine the suggested related queries for keyword ideas (chasing those keywords with new content).