If you think of the dictionary definition of a word as a big D, that will help you understand connotation or the big C. Connotation is the implied meaning or associated meaning of a word. For example, the word thin has a dictionary meaning of lean or spare, not necessarily a positive. The connotative meaning can be thin as associated with models as a positive meaning or implied meaning.
Idiom is completely different and is the hardest for non-native speakers to use. Idiom is an expression which is peculiar or characteristic to one language. For example, "fly by the seat of your pants" makes no sense by itself, yet it is an idiom which means to do something with no planning beforehand. If you think of expressions used by the people around you which by themselves really make no sense but can be explained by the speaker, you are probably dealing with an idiom.