For strategy, I also just 'drew it'. Can't say I have a strategy.
Contect-free languages are those that are (essentially) a collection of terminals and non-terminals, one of them being a starting non-terminal.
Regular languages are those that can be described by a regular expression.
So, when presented by a language, you can check whether it can be created by a regular expression or a set of productions, and in many cases, by both. They are not mutually exclusive. That, I think, is more or less the explanation that the textbook gives. Have a look at the circles on page 300.