A double negative of a verb form that is correctly used would be this:
I do not want you to go anywhere. Standard usage.
I do not not want you to go anywhere. Emphatic usage.
He doesn't want me to go. Standard usage.
He doesn't want me not to go. Emphatic usage.
Both those are used to mean, respectively, "I am not saying you shouldn't go somewhere." and "He is not telling me not to go."
That is not the same thing as a double negative where the double part is produced by a negative verb + a negative pronoun and is therefore, non-standard.
You either use a negative verb and a non-negative pronoun:
- Don't worry. I won't go anywhere.
OR
You use a declarative verb and a negative pronoun.
- Don't worry. I will go nowhere.
I am leaving aside the non-standard usages as it is too confusing to present everything at once.
Usages such as: "I don't want you to go nowhere." are non-standard.
That does not mean people do use these constructions, it just means they are non-standard. They can be dialectal, regional, local, marked as uneducated, etc.
The other answers have good links so I am not repeating them. I am merely trying to present examples clearly without any jargon.