The Langston Hughes's poem "Mother to Son" is written in free verse, so it has no formal rhyme scheme. However, there are occasional rhymes such as "stair" and "bare." The rhythm follows an informal pattern, as the poem is supposed to mimic dialogue--the way a mother would speak to her son. For example, the use of the words "ain't" and the phrase "a-climbin'" is colloquial in nature.
There are instances of alliteration, or the repetition of consonant sounds in words that are close together. For example, the lines "Bare./But all the time" repeat the "B" sound, and the line "Don't you set down on the steps" repeats the "s" sound. However, the poem makes more use of anaphora, or the repetition of words at the beginning of sentences, such as "And." The line "Life for me ain't been no crystal stair" is also repeated several times to give this idea emphasis. This poem mimics the way a person would speak, and it also includes an extended metaphor of a crystal stair--the easy path that the mother's life has definitely not followed in her hardscrabble existence.
Alliteration is when the initial consonant sound is repeated over and over. For example, think of all of your classic tongue-twisters (Peter Picked a Peck of Pickled Peppers); it is the "p" noise that is repeated over and over here. In "Mother to Son," I don't seen any good examples of alliteration. To be a good example, it would need to be several words, right after each other, at least in the same line. That doesn't really happen.
For rhyme, look to the third and seventh lines (stair/bare). The strongest of the three techniques is the rhythm. Read it out loud--it has a definite lilt and lyrical quality to it. The repetition, short phrases, dialect and metaphorical content all make the poem seem like a song or a nursery rhyme that a mother is singing to her son.
I hope that those thoughts helped; good luck!