This is something I always get confuse with (native language German). As far as I know "did + verb" is something done and finished in the past. But isn't it the same with "verb + ed"?
The normal way of talking about something in the past tense is to use "verb + ed". For example, "I finished the project on time".
You might use "did + verb" if you wanted to emphasise the point. In the previous example, if someone claimed that you completed the project late, you might say "I did finish the project on time, and here's the evidence".
Using "did + verb" where there is no doubt about the truth sounds strange to native English speakers. Saying something like "I did go shopping for food yesterday" will probably lead to the response "Well nobody said you didn't!"
"Did + verb" isn't actually it's own tense, like "has + verbed" or "had + verbed" both are. Instead, the difference is merely emphatic.
She sang in the school play.
There's no special tricks to understanding this sentence, it's exactly what it sounds like. In the school play, which was in the past, the person you're talking about sang. This just sounds like you're telling somebody a fact about another person (she), and the context of the rest of the discussion isn't really relevant.
She did sing in the school play.
The actual meaning of this sentence is still the same. She sang in the school play. However, you're now emphasizing the truth of the sentence. This is very bizarre wording if you're just stating a fact with no other context. It's likely that, if you chose to word it this way, you said something before hand, such as:
- She says she never sings in public, but back in high school she did sing in the school play.
- Her father doesn't remember, but she did sing in the school play.
- She didn't perform in the talent show, though she did sing in the school play.
The most obvious and common use will be in situations like this, where her singing in the school play provides a direct contrast to what was said immediately before, but that's far from the only time it's correct to be emphatic.
She has such a beautiful voice. After all, she did sing in the school play and the competition for the role was pretty fierce.
As a note, in all of the examples I've listed, you can just say "sang" instead of "did sing." It is not at all incorrect, it simply doesn't have the same emphasis that "did sing" does.
After I've finished typing this, it will be grammatically possible for me to say "I did answer the question", but in practice I'd only be likely to use that verb form if I was emphatically disagreeing with someone who was suggesting I had not in fact answered.
As this NGram shows, 250 years ago he did eat, for example, was actually more common than he ate. But today we normally only use this kind of do-support for questions ("Did you answer?"), for negation ("You did not answer"), and for emphatic [refutation] ("Actually, you're wrong. I did answer").
It's important to note that in the third case there (emphatic [refutation]), the word did is invariably heavily stressed. Unless it's a question or negating construction, if did isn't stressed, you probably don't want it.