what are 'auxiliary verbs'?
'There are lots of things to buy.' Auxiliary verbs are also known as 'helping verbs'.
The three most common auxiliary verbs are: “ be, do and have ”
I am leaving = Leaving is the main verb. Am is the auxiliary.
She has arrived = Arrived is the main verb. Has is the auxiliary.
Do you smoke? = Smoke is the main verb. Do is the auxiliary.

Do / does / did
Do is common for forming questions and making negatives.
Did is used for do and does in the past tense. Do and does is never used for the past.
In statements
I do my homework. You do the laundry. We do the washing up. They do yoga.
He/she does the cleaning.
In questions
Do I know you? Do you live here? Do we have time? Do they come from Vietnam?
Does he/she drive to work?
In negative sentences
I do not. (I don't) You do not. (you don't) We do not. (we don't) They do not. (they don't)
He/she does not. (he/she doesn't)
Be = am / is / are
Be can be used as an auxiliary verb or the main verb in a sentence.
Is tells us that an action is happening now or is going to happen in the future.
Be is also used to make passives.
Are is used for they and we. Was is used for the past tense of am and is.
Were is used for the past tense of you, we and they.
In statements
I am 21. You are Indian. We are waiting. They are excited He/she is cool.
In questions
Am I in the right place? Are you my new boss? Are we nearly there?
Are they the best players on the team? Is he/she old enough to go to bars?
In negative sentences
I am not. (I aren't) You are not. (you aren't) We are not. (we aren't)
They are not. (they aren't) He/she is not. (he/she isn't)

Have = has / had
Have is used to make the present perfect tense (it is always followed by the past participle).
Has is used for the third person singular.
Had is used for past tenses especially the past perfect tense. It describes an action that began in the past and continues into the present or that occurred in the recent past.
In statements
I have a dog. You have something on your shirt. We have seen it before.
They have called me three times. He/she has lived in America.
In negative sentences
I have not. (I haven't/ I've not) You have not. (you haven't/you've not)
We have not. (we haven't/we've not) They have not. (they haven't/they've not)
He/she has not (he/she hasn't)

Others
Other common auxiliary verbs are:
can, could, may, might, must, ought, should, and would.
These are also known as modal verbs. We use them to show obligation, possibility and necessity.
For example:
Jack is late. He might be sleeping. (possibility)
I should clean my room today. (obligation)
I must wear a tie to school. (necessity)
Answering questions
Auxiliary verbs are useful in giving short answers to questions.
Basically, your answer can end with the auxiliary verb.
The following examples are natural and completely acceptable ways to answer questions:
Do you like reading? Can you speak English? Do you have a sister?
Yes, I do (like reading) Yes, I can (speak English) No, I don't (have a sister)