Side note: I'm rereading Bradbury's Fahrenheit 451, in which "Dover Beach" is quoted as an example of the "danger" of books, and makes the listener cry. Very moving.
Here is the third stanza from "Dover Beach":
Sophocles long ago
Heard it on the Aegaean, and it brought
Into his mind the turbid ebb and flow
Of human misery; we
Find also in the sound a thought,
Hearing it by this distant northern sea.
While this stanza does contain a metaphor, it does NOT contain a simile (a comparison between two unlike things using the word "like" or "as").
The metaphor in the stanza is "the turbid ebb and flow / Of human misery." The two items compared are the sea and the emotions. Mental and emotional distress ("human misery") is likened to the tides of the sea ("the turbid ebb and flow") that rush in and then recede.
So perhaps the student has meant to inquire about Stanza 4 because this stanza does contain a powerful metaphor and a simile that contribute greatly to the poem:
The Sea of Faith [Metaphor = deep religious belief. Christianity is likened to a sea in an unstated comparison.]
Was once, too, at the full, and round earth's shore
Lay like the folds of a bright girdle furled. [Simile = the "Sea of Faith" is compared to a girdle as it lay "round earth's shore," supporting the world with religious faith and a unified doctrine.]
These literary devices in Stanza 4 are very effective in conveying Matthew Arnold's message of the unsettling of English tradition. The metaphor and the simile reflect the uncertainty of the Victorian Age. Industrialization altered greatly the lives of many whose livelihoods were heretofore steeped in tradition (e.g., weavers, farmers, tradesmen, etc.). New advances in scientific thought (e.g., Charles Darwin's On the Origin of Species) also certainly challenged traditional religious doctrine. With the foundations of secular and religious life altered, the world which the poet has known is now strange. It lacks unity and meaning without a "Sea of Faith"--namely, Christian beliefs--to secure it.
Thus, Arnold concludes in his final stanza that all he and his new wife can do is "be true" to each other in their love in order to provide themselves some security with their personal faithfulness.