Okay, well, if we need to find the simile and metaphor, then we should define the two terms and then explore that pesky third stanza. A simile is a comparison that uses the words "like" or "as," while a metaphor is a comparison that doesn't use those words. Now let's look at the entire third stanza of "Dover Beach":
The Sea of Faith
Was once, too, at the full, and round earth’s shore
Lay like the folds of a bright girdle furled.
But now I only hear
Its melancholy, long, withdrawing roar,
Retreating, to the breath
Of the night-wind, down the vast edges drear
And naked shingles of the world.
What a depressing stanza all about faith! I've got to tell you, though, there's more than one metaphor here, but yes, there is only one MAIN one. The metaphor that last for the whole stanza is the metaphor of faith as compared to the sea, hence the term "Sea of Faith." It is a comparison of the vast multitudes of ideas regarding faith and religion to the vastness of the ocean. As you can see, this comparison of faith to the sea is done without using the words "like" or "as."
The simile is also about faith (& the sea covering the earth). It is Faith, or more appropriately the "Sea of Faith" that used to lay around the earth "like the folds of a bright girdle furled." In other words, Faith used to be just as expansive as the ocean that extends all the way around the earth. That ocean (and that faith) was like a bright colored piece of blue fabric that could tie the earth all the way around. Note the use of the word "like" in this simile.
You can see, then, the point is that Faith is no longer girding the earth. It's a sad comparison, actually. Now it is only a "withdrawing roar." Faith is retreating. Faith is ending. (Let's hope not!)