Use "did" in the past for questions or negatives, when you are giving a short answer or when you want to be emphatic (adding emphasis). Examples: Did you eat? (question) Yes, I did. (Short answer) No I did not eat. (negative) You didn't eat? Yes, I did eat. (emphatic) Hope this helps.

The use of did is generally always a past tense confirmation or in a question. (Have you eaten? I did/did not) (Did you eat?) It's a slightly odd word in general and I'd feel it is generally a slang word but so commonly used it became a staple in casual speech.