How does connotation work to develop the theme in "After great pain, a formal feeling comes--"?
Denotation is the exact meaning of a word; connotation refers to the meanings/temperatures of the word ... what it says or suggest over and above the meaning.
In this poem, almost all of the images connote the reaction of pain as being a hardening, a stiffening, a formality in dealing with whatever realities that follow. Consider these images: ceremonious, tombs, wooden, quartz, stone, lead and freezing. In describing how one draws back in reaction to great pain, Dickinson selects images that all suggest a hardening, building a shell. She mentions the word "tombs" in the beginning of the poem, and comes around to freezing to death at the end. As we freeze, we "harden," but it happens slowly, not immediately. But the end results is the final hardening, rigor mortis.
All of this is done through the common connotation of these words, not through their denotation.
Connotation is the emotional and/or subjective meaning associated with a word. For example, we can look up a definition for the word "love." However, "love" means different things to different people; in other words, they have their own definitions for the word according to many factors.
Since Emily Dickinson's subject matter in this poem is something everyone can relate to, the readers brings his or her own experiences and biases, etc., into the reading of it. Through inserting their own meanings, the readers will be able to ascertain a theme that will vary from themes others come up with.