The exposition of the poem finds the speaker alone, tired and weary, yet unable to sleep, possibly grieving for his lost love, Lenore. He is awakened by the gentle rapping and tapping of a what he mistakenly thinks to be his dead love, Lenore. The poem goes on to reveal the "rapping and tapping" is coming from an ebony Raven, hence the title of the poem.
The main exposition in the poem is found in the early sections (mainly the first 18 lines). They set the stage, and give the speaker's background and what he'd been studying and thinking about before the knock came on his door.