<p>I know about "class having a single reason to change". Now, what is that exactly? Are there some smells/signs that could tell that class does not have a single responsibility? Or could the real answer hide in YAGNI and only refactor to a single responsibility the first time your class changes?</p>

the methods in your class should be cohesive...they should work together and make use of the same data structures internally. If you find you have too many methods that don't seem entirely well related, or seem to operate on different things, then quite likely you don't have a good single responsibility.
Often it's hard to initially find responsibilities, and sometimes you need to use the class in several different contexts and then refactor the class into two classes as you start to see the distinctions. Sometimes you find that it's because you are mixing an abstract and concrete concept together. They tend to be harder to see, and, again, use in different contexts will help clarify.