The denotation of a word is simply its definition. Whereas the connotations of a word are the ideas which are conjured when reading that specific word. Let's take the word "warm," for example. The denotation of "warm" is a comfortably high temperature. However, the word "warm" has various connotations, such as kindness and familiarity.
Always consider the word in context. In other words, in what circumstances is the word used, and to what effect? For example, if I was to write, "She has a warm heart," I want to make the point that the character is a kind and friendly person. The easiest way to remember the difference between a denotation and a connotation is to think 'd' for definition (denotation - what does the word mean?) and 'c' for conjure (connotation - what ideas are conjured by this word?)