That is a difficult question to answer, as each of those auxiliary verbs have many uses that aren't necessarily the same. In general, however, auxiliary verbs help add meaning or clarity to a sentence. For example, "did," "do," "does," and "will" make it more clear which time period you are referring to in a sentence. Which verb you use depends on the number of subjects and the time—past, present, or future—that are you are referring to. Examples: "What did the teacher do?" - in this case. "did" means the teacher has done something in the past. "What do you do?" - In this example, the first "do" makes it clear that you are asking what someone does right now. It is an action that is still in progress. "What does he do?" - In this example, "does" also refers to the present, but you are referring to someone in what is called "third person," meaning not me or you, but another person or people. "What will they do?" - In this example, "will" refers to the future. You are asking what the person you are talking to intends to do later. "Will" can be used in first (me, I, we), second (you), or third person (she, he, they). "Can," "could," "would," and "should" all mean that something might happen or that it is possible. "Can" and "could" mean something is possible, such as "I can run" or "She could hear me." "Would" is what is called conditional: if something happens first, then this will happen. Often in English, the condition is left out so it is a little confusing though. You might say "I would go to the movie if I wasn't so busy." In this sentence, "would" lets the other person know that you want to go, but you are busy so you can't. "Should" means that it would be good if something happened, but it doesn't mean that it will happen, such as "I should go finish my homework." You know you have to finish your homework, but you may decide to do something else instead. There are a lot more details and exceptions to how these verbs are used, but I think that is a good start for you to use them in practice. did - past first, second, and third person does - present third person do - present progressive first, second, and third person will - future first, second, and third person can, could, should, would - conditional

Your question actually refers to two different types of auxiliary verbs, 1) be, do, have and 2) modal verbs (or modal auxiliaries). Be, do, have are used in the structure of the verb tenses and denote time. Do = present, did= past, is/are= present, was/were= past, have = present, had= past etc. Many English verb tense forms are made up of one of these auxiliary verbs and a main verb (except the present and past simple in the affirmative form and 'to be' in the past and present simple) I don't like (present simple negative) I didn't like (past simple negative) I am doing (present continuous) I was doing (past continuous) I have done (present perfect) I had done (past perfect) etc Be, do and have are also used as main verbs. All the other auxiliary verbs are called Modal verbs. Modal verbs cannot be used alone as the main verb in a sentence. The modal verbs are can, could, may, might, must, shall. should, ought to, will, would. 'will' is used like 'be' 'do' 'have' to denote time. Will = future. It is also used for instant decisions, promises, offers and certain predictions. The rest are all used with the base form of the main verb and each is used to give additional information about the main verb such as a must, a capability, a wish, a request, or a possibility. For example Can = ability, possibility, a request, asking for permission. Could = Asking for permission, request, future possibility, suggestion, ability in the past. For more examples and explanation of the use of be, have, do and the modal verbs see http://grammar.ccc.commnet.edu/grammar/auxiliary.htm

Try studying. Most courses, in fact all of them, teach you this stuff.