A short answer is a reply to a yes/no question that includes a subject pronoun and an auxiliary verb. In English, answering with just yes or no often sounds too blunt or even rude. Adding a short form makes the response natural and polite.
The formula is always the same: yes/no + subject pronoun + auxiliary verb. You never repeat the main verb or any other part of the question.
How it works
The auxiliary in the short answer comes directly from the question. If the question uses do, the short answer uses do. If the question uses can, the short answer uses can. The subject pronoun matches whoever the answer is about -- and it may change from the question. If someone asks Do you...?, the answer uses I (or we).
Nothing else goes into the short answer. The main verb, the object, and everything after the auxiliary are dropped.
With do, does, did
Questions in the present simple and past simple use do, does, or did as the auxiliary. Short answers repeat that same word.
With be
When the question uses am, is, are, was, or were, the short answer repeats the same form of be.
With have (perfect tenses)
In present perfect and past perfect questions, the auxiliary is have, has, or had.
With modal verbs
Questions with can, could, will, would, should, may, and must follow the same pattern.
The contraction rule
This is the rule that causes the most mistakes. In positive short answers, do not contract the auxiliary with the subject. In negative short answers, contractions are normal and expected.
Positive -- no contraction:
Negative -- contraction is fine:
The reason is practical: a contracted positive form like Yes, I'm or Yes, she's sounds incomplete to a native speaker, as if the sentence was cut off mid-thought. The full form signals that the answer is finished.
Switching the subject
When someone asks you a question, the answer usually switches to I or we. When someone asks about I, the answer switches to you. The auxiliary may need to change form as well.
With third-person subjects, the pronoun stays the same or is replaced by the appropriate pronoun.
Common mistakes
Contracting positive answers
Adding the main verb
Wrong auxiliary
Answering with just yes or no