What are the figures of speech in the poem "A Mile with Me" by Henry Van Dyke?

The entire poem is an extended metaphor, or analogy, comparing the speaker's lifetime to a journey of "a mile." To describe this long journey as a mere mile is an understatement. This journey is sometimes a "merry way" and sometimes a "weary way," which are further represented by the metaphors "summer sunshine" and "winter rain," respectively. In describing the happy seasons of life, the speaker wraps together personification, a simile, and pathetic fallacy. The speaker wants the desired friend to let his "frolic fancy play," that is, the friend's imagination (fancy) is personified as being able to play "like a child," which is a simile, "through the flowers gay." Ascribing emotions to parts of nature is a pathetic fallacy, a figure of speech that is like personification but specifically uses nature to reflect the emotion the author wants to convey. Flowers can't literally be "gay" or happy, but describing them as such helps the author create the desired mood. 

In the second stanza, the speaker melds together symbolism and metaphor to describe the "weary way," or the difficult periods of life during which he desires companionship. First, "heart" is used in its symbolic sense as the seat of the emotions. The heart of the desired friend will have "eyes to see." This is a metaphorical way of describing insight and understanding. However, describing a heart having eyes is an unusual paradox if taken literally; hearts can't have eyes. The speaker wants his friend to have emotional understanding of "stars [that] shine out o'er the darkening lea." This phrase is also symbolic; the stars represent hope, and the dark meadow (lea) represents misfortune or despair. Thus the speaker wants a friend who can help him find hope in the midst of despair or during a life crisis.

In addition to the plethora of figures of speech in the poem, the poem also uses a consistent iambic rhythm with similar line lengths that support the idea of a long and steady walk. The rhyme scheme uses only two rhymes for the first two stanzas, interwoven, which gives the poem an even greater feeling of consistency--the type of consistency the speaker is looking for in his friend for life.