Will and shall are modal verbs. Lesson 27 shows you how to make correct sentences with them. This lesson shows you when to use them. Notice that we use shall only for 1st person (Lesson 2); -'ll is the short form for both verbs.
We shall all die one day.
Do you think it will rain tomorrow?
The manager will be writing to you soon.
I'll be phoning him tonight.
NOTICE: ALSO be going to, present simple, present continuous: Lesson 41 shows you the differences between them
Don't phone now! They'll probably be having lunch. They usually have lunch at this time.
EXAMPLE: By this time tomorrow, I'll have finished all my exams.
He's next door. Just a minute and I'll get him for you.
If you think it's a good idea, I'll phone him.
Shall I help you with that?
Will you mail this for me?
What shall I say to her?
NOTICE: could (Lesson 29) is more polite
The car won't start. ( = will not)
He won't tell me the answer.
We'll never forget your kindness.
I'll kill you if you do that again.
I think I'll visit my parents this weekend.
I'll have coffee, please.
NOTICE: do NOT use be going to (Lesson 37)