Auxiliary verbs are conjugated depending on the subject of a sentence. Here are a few examples of auxiliary verbs:
Tom has lived in Boston for twenty years.
They didn't come to the party last night.
I was cooking dinner when you telephoned.
What are you doing tomorrow afternoon?
Knowing correct auxiliary verb usage is key to tense usage. Every tense takes an auxiliary form of the verb. There are three exceptions to this rule:

1. Simple present positive: She works at a bank.
2. Simple past positive: He bought a new TV last week.
3. Positive imperative statements: Hurry up!

There are also a number of short forms that take ONLY the auxiliary form of the verb:

• Yes / No answer short forms: Do you live in England? - No, I don't.
  Has she been to Paris? - Yes, she has.
  
• Question tags: They enjoy learning English, don't they?
  He won't agree with me, will he?
  
• Positive agreement / inclusion: I went to the beach last weekend. - So did I.
  I'm working very hard at the moment. - So is she.
• Negative agreement / inclusion: They haven't worked here long. - Neither have I.
  We won't be able to come next week. - Neither will I.

Here is a quick overview of auxiliary verb usage:
DO / DOES
Used simple present question and negative forms:
What time does he get up?
They don't drive to work. They take the bus.
DID
Used in simple past question and negative forms:
When did they arrive yesterday?
He didn't finish his homework last week.
IS / ARE / AM
Used in present continuous and for the future with 'going to':
They are working hard at the moment.
She is going to study medicine at university.
WAS / WERE
Past continuous:
I was watching TV when you arrived.
What were they doing while you were cooking dinner?
HAVE / HAS
Present perfect and present perfect continuous:
How long have you lived here?
I've been working since seven this morning.
HAD
Past perfect and past perfect continuous:
He had eaten by the time I arrived.
She had been studying for two hours when he finally telephoned.
WILL / WON'T
Future with 'will':
What will the weather be like tomorrow?
He won't understand.
If you don't understand all of these tenses, don't worry. This overview chart shows the positive, negative and interrogative (question) forms of all the principal tenses in English with a brief description of the principal usage. The timeline tenses chart provides a handy visual reference sheet to English tenses and their relationship to the past, present and future. Included you will find active, passive, simple and continuous forms positioned according to their occurrence in time.