What literary and figurative devices are used in "Birches" by Robert Frost?

Like most of Robert Frost's poems, "Birches" uses a steady meter, in this case a classic "blank verse" of 10 syllables per line.   Frost once said that writing poetry without a set meter (free verse) would be like playing tennis without a net.

Some of the figurative devices in this poem are as follows.

a) Metaphor (comparisons that do not use the word "like" or "as"):

the stir cracks and crazes their enamel.

(The branches of birch trees are not made of enamel, of course.  The poet is comparing their hard, iced-over surface to enamel.)

Soon the sun’s warmth makes them shed crystal shells
Shattering and avalanching on the snow crust—
Such heaps of broken glass to sweep away

(The poet compares bits of broken ice to "heaps of broken glass".)

b) Alliteration (The repetition of initial consonant sounds)

They click upon themselves
As the breeze rises, and turn many-colored
As the stir cracks and crazes their enamel.
Soon the sun’s warmth makes them shed crystal shells
Shattering and avalanching on the snow crust—

(In these 5 lines, a total of 6 words begin with a hard "c" sound.  Perhaps the poet wants to imitate the clicking of the ice-covered branches, in which case it is an example of onomatopoeia.)

c) Simile (Comparison using the word "like" or "as")

trailing their leaves on the ground
Like girls on hands and knees that throw their hair
Before them over their heads to dry in the sun.

d) Personification (speaking about inanimate objects and concepts as if they were human)

I was going to say when Truth broke in
With all her matter of fact about the ice storm,

("Truth" is referred to as a female person who interrupts one's thoughts.)

e) Anaphora (the repetition of words or phrases)

One by one he subdued his father’s trees
By riding them down over and over again
Until he took the stiffness out of them,
And not one but hung limp, not one was left
For him to conquer. He learned all there was
To learn about not launching out too soon
And so not carrying the tree away
Clear to the ground.

(In this little section, the words "one" and "not"  are used 4 times each.)

What poetic devices, other than rhythm and structure, are used in "Birches" by Robert Frost?

Yes, there are other poetic devices being used in addition to rhythm and meter, but I'll start with rhythm and meter.  

The poem is mostly written in iambic pentameter.  An iamb is a type of metrical foot, and it is a two syllable unit.  The first syllable is an unstressed syllable, and the second syllable is a stressed syllable.  In "Birches," many lines have five iambic feet.  That's why it is iambic pentameter.  There are 10 syllables per line, and the syllables alternate between unstressed and stressed syllables.  I can use bold to indicate the stressed syllables from an early line of the poem to illustrate.  

I like to think some boy's been swinging them. 

As for the rhyme scheme of this poem, Frost wrote this poem in blank verse.  Blank verse doesn't use rhymes, and it is a form that is commonly used in long narrative poems.  

Alliteration is another poetic device that "Birches" uses.  Alliteration is the use of repeated consonant sounds at the beginning of words that are placed near each other.  Line 10 has a good example of alliteration with the letter "s." 

Soon the sun's warmth makes them shed crystal shells 

Another poetic device that this poem uses is personification.  Personification gives human characteristics to an object, animal, or abstract idea.  For example, line 21 says that "Truth broke in."  The following line even uses the pronoun "her" to further emphasize the humanity of "Truth." 

There are a couple of wonderful similes in the poem as well.  A simile makes a comparison between two unlike things by using the word "like" or "as."  My personal favorite from the poem is the following line.  

And life is too much like a pathless wood

I like hiking, and the comparison brings a very familiar image to my mind.  Another simile in the poem compares a tree's drooping branches and leaves to a girl crawling on the ground with her hair dangling beneath and dragging on the ground.  

You may see their trunks arching in the woods 

Years afterwards, trailing their leaves on the ground 

Like girls on hands and knees that throw their hair 

Before them over their heads to dry in the sun. 

What do the literary and poetic devices in "Birches" demonstrate?

There are many poetic and literary devices in "Birches." When considering why the poet has made those choices, it's important to consider the overall tone or statement the author is making through the poem. This poem's tone is actually interpreted quite differently depending on a reader's personal experience. Some interpret this as lighthearted, and others see a darkness of spirit. You'll need to determine where you see evidence to support a particular tone. I'll share with you my own interpretation and some of the literary devices for that interpretation so that you can construct your own meaning.

Here's where I would begin: In this poem, Frost uses imagery and poetic devices to show the bittersweet nature of life.

The birches in winter are presented with both peaceful and destructive imagery. On one hand, the ice-laden birches are described in tones of warmth and beauty:

They click upon themselves
As the breeze rises, and turn many-colored
As the stir cracks and crazes their enamel.

They "click" and capture light in many colors, reflecting an easy and serene tone. But as they capture light, a transformation occurs:

Soon the sun's warmth makes them shed crystal shells
Shattering and avalanching on the snow-crust—
Such heaps of broken glass to sweep away

In this imagery, we also see how light can destroy, turning beauty to "broken glass" after it "shatters" the shell of peace. In this section, you can also hear the rustling of all that ice in the birches in the alliteration of the "s" sound, noted by use of bold above.

The speaker himself notes the childhood glee in climbing to the top of a birch tree and swinging back to earth:

Then he flung outward, feet first, with a swish,
Kicking his way down through the air to the ground.

He was "once a swinger of birches," able to leave the cares of the world and stand with poise above it high in the branches of birch trees. But he also notes that the birches themselves have the power to cause pain:

and one eye is weeping
From a twig's having lashed across it open.

Thus, the birches are again transformed from an image of simple peace and escape to an instrument of possible pain, symbolized by the twig that has cut his eye open, leaving him "weeping."

Note the contrasting images of light and darkness in this line describing the birches:

And climb black branches up a snow-white trunk

The same tree is both "black" and "snow-white." Darkness often symbolizes sadness or evil, and "snow-white" often symbolizes innocence and purity. Therefore, this experience provides both a path toward sadness and a path toward innocence.

And this is the bittersweet nature of life. Moments of peace and tranquility are often shattered around us by an unexpected "light," or knowledge. To live is to experience both the black branches and the white trunk of climbing "toward heaven," embracing the experiences that make life "good both going and coming back." Frost uses various literary devices in "Birches" to show these conflicting images of life.