Helping verbs are the key to many structures; often the word that needs to change when altering the structure of a sentence is the helping verb (or the 1st helping verb if there are multiple).
As a main verb, be is used to equate or classify the subject with another noun or with an adjective. Unlike other verbs, be is treated like a helping verb even when it’s the main verb (unless other helping verbs are present).
As a helping verb, be is used before an -ing verb for the future be going to and for progressive/continuous tenses.
In British English, the verb have got is used to show what the subject owns, holds, includes, etc. (although in American English, have is used alone). In this case, have is treated as a helping verb.
Have is also the helping verb used before the main verb in perfect tenses.
Since there are some structures in which a helping verb is necessary, do exists to fill that role when no other helping verbs fit in such sentences. Do is most often used for negatives and questions in the present simple and past simple tenses.
Do can also be a main verb, but as one it cannot act as a helping verb.
Can shows what the subject is able to do or what they are allowed to do. The equivalent could is used for the past or to be polite. Neither changes due to subject or tense.
Will is used to express future expectations or sometimes future plans. Would is typically used for requests. Neither changes due to subject or tense.