Will

(in future tense)

I will be there.

(in requests)

Will you do it for me?

Won't

(negative of will)

No, I won't.

Can

(to indicate ability)

I can do it.

(in requests)

Can you help me?

(informally to ask permission)

Can I use your phone?

Can't

(negative form of can)

No, you can't.

May

(to indicate possibility)

I may go to New York.

(to ask permission)

May I help you?

Could

(to indicate past ability)

He could play cards well.

(to indicate possibility)

I could give you a ride.

(in requests)

Could you open the door please?

(to ask permission)

Could I use your restroom?

Couldn't

(negative past tense)

I couldn't help it.

Should

(to express obligation)

I should go to the wedding.

(to conjecture)

He should be in Miami by now.

Shouldn't

(negative suggestions)

You shouldn't do that.