Auxiliaries are a group of verbs that can be placed before 
main verbs to form expanded verbs.  In an expanded verb, the
auxiliary shows tense (past or present) and person (singular or
plural).  The main verb shows the action or state being described. 
Expanded verbs are used to form questions and negatives, to make
predictions and express uncertain conditions, and to show certain
time frames (tense).  
     There are four groups of auxiliaries in English: the DO group,
the MODALS, the HAVE group, and the BE group.  The form of the main
verb depends on which group the auxiliary that precedes it belongs
to.  The chart below illustrates the four auxiliary groups and the
verb form(s) that follows each of them.

The DO group: A form of Do followed by the base form of a verb is 
used to form a question or a negative statement:

e.g., I eat ice cream ===> Do I eat ice cream?
or ===> I do not eat ice cream.

     If there is already an auxiliary in a statement, use that
auxiliary instead of Do to form a question or negative from that
statement:

e.g., She is eating ice cream ===> Is she eating ice cream?
                          or ===> She is not eating ice cream.

Do is also used to add emphasis to a positive statement:

e.g., I hate vegetables, but I do eat them.

The MODALS: A modal plus the base form of a verb is used to speak
about a future time, to make predictions, express uncertain
conditions, or show politeness:

e.g. We will eat dinner at 7pm.
     
     He promised that he would be home for dinner.
     
     I might be unable to finish my work on time.

     Would you call me if you are going to be late, please?

     Note that all modal forms may be used in present time frames:
 
e.g. I think I will go.
     I think I might go.
     I wish I could go.

     However, only would, could, might, and should can be used in
past time frames:

e.g., He said he would go.
      We thought you should know.
      He knew they could do it.

The HAVE group: A form of Have followed by the -ed/-en form of a
verb is used to show that an action began prior to the main time
frame of a passage.  Have and has are used for action beginning
prior to the present.   Had is used to show action beginning prior
to a time in the past.

e.g., They have lived in New York since 1989.

      By 1986 we had lived in six different cities. 


The BE group: After auxiliaries of the Be  group, there are two
possible forms of the main verb.  

Be + -ing is used to show that an
action is going on at a particular moment or continuing throughout
a period of time:

e.g., They were eating dinner when the phone rang.

      We are learning to cook from our dad.

Be + -ed/-en is used to show that action of the verb is not
done by the subject.

e.g., I was taken to a dance on my 16th birthday.


Materials adapted from A Tapestry Grammar, Heinle