There is one issue that is also for German native speakers quite difficult; the thing with the double negation. Often heard - at least in movies is:

I didn't do nothing. This means that this person wants to say I didn't do anything. or I did nothing (wrong).
To say I didn't do nothing (or I ain't doing nothing) does not really get great points for style, still is clear that this is a negative sentence and it's clear what it means.

Now let's look at the German way. The Germans use the mathematics for their negation which means that two minuses makes a plus => two negations make a positive sentence.

I did not do nothing = Ich habe nicht nichts getan. Ich habe nicht nichts getan = I did something.

Does this sound illogic to you? Well, it only tells you to be careful how many negations you put in a sentence, because the mathematical system is continued. Three negations make it negative again, four make it positive etc. My advice: just stick to one negation, that's the easiest and understandable way also for German.

This principle of double negation also works with the general negative words like

never = nie nobody = niemand

Again the English can be still understood as a negative sentence even though we have to admit that it doesn't sound so nice. Just for demonstrating purposes:

Nobody said nothing = Niemand sagte nichts.

The German sentences gives the association that if nobody said nothing, then all were saying everything. This actually doesn't make much sense. Still that's the way it goes.

Anyway the English grammar works actually the same. If there is Nobody, No one, None in a sentence there is no extra negation. The correct English would say: Nobody said anything. = Niemand sagte etwas. And we are in clear waters again. The only useful general advice we can give it: stay away from double negations - they are really confusing to everybody in any conversation.