In English there are differing usages of 'double negatives' that you describe in your question. People can often use it in a joking and playful way, often to obscure information, for instance riddles and jokes. This should usually be obvious from tone of voice, behaviour, context and so on.
In the example you cite, and in the majority of cases in which double negatives are used, it should not be taken literally. That's to say, the confusing logical structure of the sentence is not intentional, like it would be in, say, a riddle. Instead, it is a common mistake common in many dialects, and should basically be ignored.
If we parse the following commonly used phrase:
"I ain't done nothing wrong."
We would find that the literal meaning is that the person in question has done something wrong. This is absolutely not the intention of the speaker, unless this is an uncharacteristic phrase to them in which case it may be to wriggle out of guilt by obscuring the true meaning of their sentence. Instead it should be read simply as if the author is saying "I haven't done anything wrong.".
If we take a look at the specific example you cite:
"Life for me ain’t been no crystal stair."
This is again a phrasing common to particular dialects. To me it sounds more American than English, but it is not possible to tell exactly. To firstly find the meaning of the actual logic of the sentence, we apply the same technique as above: we ignore the double negatives, and take it as a single negative.
The sentence then becomes:
"Life has not been a crystal stair for me."
The bit about 'a crystal stair' is simply a metaphor for a perfect life, and so the sentence really means that for whomever is speaking, life has not been perfect for them.
In fact, in the poem from which your phrase comes, it is likely used as a warning from the mother to the son, warning of the hardship to come in adolescence and adulthood (or simply life in general).