We use auxiliary verbs to form different verb tenses and aspects.
DO and DOES
We use do to form negatives and questions in the simple (habitual) present. (Remember, if the subject is 3rd person singular--he, she, it--use does.) The main verb after do/does is in the root (simple) form.
Barack Obama does not live in Chicago now.
(In speech, you can contract does + not => doesn't)
I do not understand Arabic.
(Contraction: do + not => don't)
Where do you live?
Does Mary attend classes at the University of Maryland?
We use the past tense of do--did--to form negatives and questions in the simple past.
We use did for all persons. The main verb after did is in the root (simple) form.
The contraction of did + not => didn't.
Jack did not do his homework.
Did the teacher write the homework on the board?
We use be as an auxiliary verb to form the present and past progressive (continuous). Use the present form (am, is, are) for the present progressive. use the past form of be (was, were) for the past progressive. The main verb after any form of be is in the present participle (Ving) form.
Remember! Both do and be can also be main verbs.
The students do their homework.
The students are in class every day.
In this video, Paul talks about the auxiliary verbs do and be and main verbs: