Definition:
Modal Auxiliaries are also known as Helping Verbs.

Auxiliaries:

1.Can and Could

2.May and Might

3.Shall and Should

4.Will

5.Must and Ought to

6.Dare

7.Need

Can And Could:
Can and could is used to express ability, capacity and  capability.

Can is used in Present Tense

EX:
1.Tom can run fast if he likes
2.I can answer this question

Could is used in Past Tense

EX:
1.Sonia could run fast if she tried
2.Sam could do well in the examination if he worked hard

Can and Could are also used to make a request

Can:

1.Can I use your pen to write a letter to my brother ?

2.Can you help this poor man with some money and material

Could:

1.Could I use your telephone to ring up my papa ?

2.Could you please check up your accounts.

Note: could is more politer than can

May And Might:

Might is used in the Past Tense in place of May

EX:
1.He asked me if he might go there.

May and Might are used to express Permission

EX:
1.May I come in, sir?
2.Might I come in, sir?

May is also used to express wish, prayer or curse
EX:
1.May God bless you. (prayer)

2.May you succeed in your new venture! (prayer)

3.May I have a look at your album of postage stamps. (wish)

4.May he die. (curse)
Note: Might’ is more politer than ‘May’ but its usage in this sense is less common.

Shall And Should:

Shall is used with the 1st person singular & plural in the Future Tense

.
EX:
1.I shall go there to participate in the painting contest

2. We shall go to bazaar to buy some stationary items.

Should is used in the Past Tense in the place of shall

.
EX:
1.He told me that he should do his duty

Shall is also used as threat.

EX:
1.The miscreant shall be punished.

2.You shall have to apologize.

Should is used to express duty or obligation

EX:
1.You should do your duty. (duty)

2.You should keep your promise. (obligation)

Will And Would:

Would is used in the Past Tense in the place of will.

EX:
1.She told us that she would not tell a lie.

Will is used with 2nd & 3rd person singular & plural in the Future Tense.

EX:
1.They will go on a picnic next Sunday.

2.He will dance in the party if he is asked to do so

Would is used to express a Wish

EX:
1.Would that I were a King!

2.Would that I were a billionaire

Must And Ought To:
Must and Ought to used to express duty or obligation, determination, expectation and probability.

Must:
1.You must obey your elders. (duty)

2.You must win this match. (determination)

Ought To:
1.You ought to love your country. (obligation)

2.Anitha ought to stand first in her class. (probability)

3.Leena ought to come soon (expectation)

Dare:
Dare is used to express courageousness
EX:
1.How dare you touch me ?

2. How dare you tell me Stupid ?
Note: When ‘dare’ is used as an auxiliary never use ‘to’ with it. But when it is used to challenge somebody, ’to’ is used after it.

Need:
‘Need’ is used to express some necessity or obligation, generally in an interrogative sentence in the Present Tense
EX:
1.Need I give you more assurance after what I have already promised ?

2.Need I speak more words after what I have already said in the plan ?

thats all folks.....

Thankyou,
Rajkumar