What are the metaphors and similes in "The Solitary Reaper"?

The imagery in this poem is very vivid, but the presentation of it can indeed make it difficult to identify the figures of speech. A metaphor is a device whereby a comparison is drawn between two things by implication, rather than by saying something was like something else (which would be a simile). In this poem, then, we can see indirect comparisons made between the singing girl, the solitary reaper of the title, and the nightingale and cuckoo-bird. The speaker uses fanciful imagery to express how these birds' song fits into the scenarios in which he places them: the nightingale sings a soothing song to "weary" travelers, while the cuckoo's springtime song is a "thrilling" break in the silence. By inference, then, we can assume that the speaker feels a similar connection to the reaper's song. It is a beautiful, welcome break in the silence, unexpected and yet a balm to him.
The only device in the poem which could be considered a simile is in the final stanza, in which the maiden is said to sing "as if her song had no ending." We can deduce from this that she is singing like a person whose song was endless; as if this were her only task and she could do it forever. This both gives the impression that the girl felt naturally part of the scene as a whole, and also that her singing seemed effortless.

A metaphor is a comparison that does not use the words "like" or "as." A simile is a comparison that does use those words.
Wordsworth uses several metaphors for the reaper. The solitary reaper is a woman who is alone in a field in the Scottish Highlands reaping and singing when the narrator comes across her. He likens her to both a "Nightingale" and a "Cuckoo-bird," both birds with beautiful songs. However, we are told that the reaper's song is more lovely than either of theirs.
The sole simile in the poem is the following:

the Maiden sang
As if her song could have no ending

Here the reaper's song is compared to something unending. This is a bit of a stretch as a simile, but comparing the song to the eternal helps make Wordsworth's point: the poem's narrator is trying to emphasize that the solitary reaper is a natural being, like a bird—something at one with her environment, and a wild, unchanging being. This romanticizes, or makes beautiful, the hard labor this woman is performing.