Before we can discuss the tone used in any specific poem, we need to establish what tone is in the context of poetry. In a nutshell, tone is the general attitude of the writer as depicted in the words and structure of the poem. In other words, the tone is the character of the poem. To provide a few generic examples before discussing the poem at hand, a poem can be cheerful, somber, humorous, formal, informal, admiring, or critical.

I would argue that the tone used in this particular poem is colloquial and instructional. Since this is a mother speaking to her son, it is quite natural for her to use a colloquial tone, and this tone comes across thanks to the use of incomplete words such as “a-climbin’,” “reachin’,” and “turnin'," She refers to her son as “boy,” which is a colloquial term of endearment. She speaks in her natural voice with no pretense or inhibitions, using the word “I’se” instead of “I am,” which adds to the colloquial feeling of the poem.

Through her colloquialism, however, the speaker is issuing her son with firm instructions. After using an extended metaphor to describe the difficulties she has faced in life, she issues her son with three instructions: “don’t you turn back,” “don’t you set down on the steps,” and “don’t you fall now.” The mother’s determination to provide her son with encouragement and teach him about life creates an instructional tone.

Tone is defined as the attitude of the author about a subject, as seen in the perspective and language used to explore that subject in the writing. In the poem "Mother to Son", Langston Hughes explores the subjects of life and resiliency. To that degree, the tone can be considered resilient or gritty.

Its had tacks in it, and splinters, and boards torn up. And places with no carpet on the floors, bare. But all the time, i'se been climbing on, and reachin landins and turnin corners, and sometimes, doing in the dark where there ain't been no light.

In the above text, the mother is using the extended metaphor to explain her ability to bounce back after trials, and she uses her hardships to motivate and inspire her son to continue fighting. This mother's drive and determination, even after challenges have mounted, displays her resilience and grit. 

Another possible tone of this poem is didactic. Didactic literature is defined as informational or instructional, usually explaining a truth or moral. While the definition implies a boring connotation, this is not always the case for didacticism. In fact, and is the case in, Mother to Son, the urgency of this mother's truth, keeps the poem from ever being described as boring.

...so boy, don't you sat down on them steps, cause you finds its kinda hard. Don't you fall now, for i'se still climbin on, and life for me ain't been no crystal stair. 

To add to the previous answer, the tone of the poem can also be characterized as plain, homely, colloquial. This is apparent from the use of such words as 'ain't' and phrases like 'I'se still goin' honey'. Obviously this kind of tone is suitable to the situation, where a mother is familiarly addressing her son.

The tone also becomes increasingly hortatory throughout, that is to say, the mother is exhorting her son never to give up in life. Such lines as 'Don't you fall now' are actually in the imperative form, or the form of a command. She is actually ordering him to never give up the fight.

Although on the face of it it's a fairly leisurely poem, it contains an urgent message at its heart. Also, although it may appear rather plain in style, it is rather disingenuous in its apparent artlessness, as it is built round an extended metaphor, or conceit: that of life as an toiling journey up a set of stairs. The sense of upward movement is crucial; the mother is anxious for her son never to give up the climb, no matter how hard it may sometimes be, as it has been for her. She aims to teach him by her own example. 

The tone of "Mother to Son" is didactic.  A mother, after looking back at her life, wants her son to know that life is not easy or glamorous--it's not a "crystal stair." Instead, the mother/speaker chooses to describe her life as a winding, unrelenting staircase.  However, the poem does not imply a negative tone toward life as a whole.  The mother states that even though her life has not been facile, she has been "reachin' landin's," "turnin' corners," and "sometimes goin' in the dark." This implies that she wants her son to press on even when he does not know what lies ahead of him. 

The last several lines of the poem definitely illustrate an inspirational tone.  The mother admonishes her son not to fall down because she's "still climbin'."  If she can continue on her ardous journey after all these years, then surely her son can gain encouragement from his mother's example.