Sometimes I never know if I should say nothing or anything.
For example: Should I say
I don't have nothing to do
I don't have anything to do
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Standard English (from whichever country) does not allow another negative word (no, nothing, nobody, nowhere, never, etc) within the scope of "not": use the corresponding "any" form instead.
Many colloquial varieties of English all over the world do allow this, and many people say "I don't have nothing to do". But at the same time, many speakers don't use such forms, and some judge people harshly who do so.
Nothing = not anything
You use the pronoun nothing to express an absence of things. As it already has a negative word "no" in it, you don't use another negative before or after it. So the sentence:
I have nothing to do = I don't have anything to do.
However, the "nothing" is stronger and more definite than "not anything".