"I won't not use no double negatives."
— Bart Simpson
Ah, yes, the wise words of Bart Simpson. Using a double negative doesn't always turn a negative statement into a positive one. However, it can lead to a confusing sentence.
An exception to this rule is to follow the word "not" with an "un-" statement if you are attempting irony, sarcasm, or an understatement. For instance, you could say, "I'm not unhappy" to show that you are not totally happy.
It is best to stick with positive statements, as they will be more clear and to the point. They will make your writing feel crisp. Negative words can come across as being indirect, which may make it more challenging for your reader.