Use I'll + base verb to offer help at the moment you speak. (I'll = I will.)
I'll help (offer)
That bag is heavy. I'll carry it.
I'll help you.
I'll open the door.
Try it: Lani: I can't open this box. Diego: ___ do it for you. Finish what Diego says. (I'll / He'll / They'll) Answer: I'll — Diego is the one offering, so the offer is about himself: I'll. Saying "He'll" or "They'll" puts it on somebody who is not speaking.
I'll have tea (decide now)
Use I'll + base verb when you decide something at this moment, not before.
I'm thirsty. I'll have some water.
Okay, I'll take the bus.
I'll call you later.
Not "I'm thirsty. I have some water." — say "I'm thirsty. I'll have some water.". You decide as you speak, so use I'll + base verb.
Try it: Sofia: Are you hungry? Farid: Yes. ___ a sandwich. Finish what Farid says. (I'll make / I make / I making) Answer: I'll make — Farid decides as he speaks, and a decision made right now uses 'll. The plain form is about what he does in general.
It'll rain (predict)
Use 'll + base verb to say what you think will happen. (it'll = it will; they'll = they will.)
I think it'll rain tomorrow.
Don't worry. It'll be fine.
They'll be happy.
Try it: Wei: The wind is very cold today. Amina: ___ snow tonight. Finish what Amina says. (It'll / I'll / We'll) Answer: It'll — Amina is saying what she thinks will happen, and for weather we say It. Saying "I'll" or "We'll" would be about people.
Same for everyone (no -s)
Will ('ll) never changes. He, she, it use it too: he'll, she'll, it'll, they'll, never adds -s.
I'll come.
She'll come.
They'll come.
Not "She wills come." — say "She'll come.". Even with she, it stays will ('ll), never wills.
Try it: Yasmin: These boxes are heavy. Mei: Hiroshi ___ help you. Finish what Mei says. (will / wills / will to) Answer: will — Will never changes, even for Hiroshi — there is no "wills".
Keep the verb plain
After will ('ll), the verb stays plain. No -s, no -ing.
He'll come at six.
She'll help you.
It'll rain later.
Not "It will rains." — say "It will rain.". After will, use the base verb: rain, not rains.
Try it: Camila: Is Mei coming? Lars: Yes, she ___ the bus at eight. Finish what Lars says. (will take / will takes / will taking) Answer: will take — The verb after will stays plain, even for she — not takes and not taking.
No 'to' after will
Don't put to after will. Say I'll help, not "I'll to help".
I'll help you.
She'll call later.
We'll wait here.
Try it: Matilda: The window is open and it is cold. Mateo: I ___ it. Finish what Mateo says. (will close / will to close / will closing) Answer: will close — Nothing goes between will and the verb — no to and no -ing.
Won't (say no)
To say no, use won't + base verb. (won't = will not.)
Don't worry. I won't be late.
She won't come today.
They won't forget.
Not "I don't be late." — say "I won't be late.". To say no about later, use won't, not don't.
Try it: Yasmin: Please don't tell Lars. Ethan: OK, I ___ say anything. Finish what Ethan says. (won't / don't / will) Answer: won't — Ethan is promising about what comes next, and the negative of will is won't. One answer is about now, and one says the opposite of what he means.
Will you...? (ask)
To ask, put Will first: Will you help me? Short answers: Yes, I will. / No, I won't.
Will you help me?
Will you open the door?
Will she come? — Yes, she will.
Try it: Hiroshi: ___ you write to me from Senfarren next week? Liam: Of course I will. Finish what Hiroshi asks. (Will / Did / Do) Answer: Will — Hiroshi is asking Liam to do something later, and Liam agrees — so the question opens with Will. One answer asks about the past, and one is about what he does in general.
Use it
Put it together: 'll for an offer, a decision now, or what you think will happen. won't to say no. Will you...? to ask.
I'll answer the phone.
It'll be cold tonight.
Will you wait for me?
Try it: Lani: Are you ready for the test? Wei: Yes. It ___ be hard. Finish what Wei says. (won't / doesn't / not will) Answer: won't — Wei is saying what he thinks about a test that has not happened yet, and the negative of will is won't. "Doesn't be" is not English, and "not will" puts the words the wrong way round.