How would I say, for example, "I couldn't find any food"?
If you want to sound formal, I'm thinking of
Je n'ai pas trouvé la moindre nourriture
Je n'en ai pas le moindre doute
If you want to sound casual, like anyone in France (because the above answer if very fancy), you should go for :
Je n'ai pas trouvé de nourriture.
Just put nothing. I don't feel like this is any different from the affirmative form.