We use I’ll (= I will) when we decide to do something at the time of speaking:
Oh, I felt the door open. I’ll go and shut it.
“What would you like to drink?” “I’ll have some orange juice, please.”
“Did you call Julie?” “Oh no, I forgot. I’ll call her now.”
You cannot use the simple present (I do / I go, etc.) in these sentences:
I am a little hungry. I think I’ll have something go eat.
I don’t think I’ll go out tonight. I’m too tired. (not I think I won’t go out …)
In spoken English, the negative of will is usually won’t (= will not):
I can see you’re busy, so I won’t stay long.
Do not use will to talk about what you have already decided or arranged to do
I’m going on vacation next Saturday. (not I’ll go)
Are you working tomorrow? (not Will you work)
We often use will in these situations:
Offering to do something
That bag looks heavy. I’ll help you with it. (not I help)
Agreeing to do something
A : Can you give Tim this book?
B : Sure, I’ll give it to him when I see him this afternoon.
Promising to do something
Thanks for lending me the money. I’ll pay you back on Friday.
I won’t tell anyone what happened. I promise.
Asking somebody to do something (Will you …?)
Will you please be quite? I’m trying to concentrate.
Will you shut the door, please?
You can use won’t to say that somebody refuses to do something:
I’ve tried to give her advice, but she won’t listen.
The car won’t start. (= the car “refuses” to start)
Shall I …? Shall we …?
Shall is used in the question Shall I …? / Shall we …? to ask somebody’s opinion
(especially in offers or suggestions):
Shall I open the window? (= Do you want me to open the window?)
“Where shall we have lunch?” “Let’s go to Marino’s”
We use should more often in the same situations:
Should I open the window? (= Do you want me to open it?)
Where should we have lunch?