will or would:-

We use will:

• to talk about the future – to say what we believe will happen
• to talk about what people want to do or are willing to do
• to make promises and offers

would is the past tense form of will. Because it is a past tense it is used:

• to talk about the past.
• to talk about hypotheses – things that are imagined rather than true.
• for politeness.

Beliefs:-

We use will

• to say what we believe will happen in the future:

We'll be late.
We will have to take the train.

We use would as the past tense of will:

• to say what we believed would happen:

I thought I would be late …… so I would have to take the train.

Offers and promises:-

We use I will or We will to make offers and promises:

I’ll give you a lift home after the party.
We will come and see you next week.

Willingness:-

• to talk about what people want to do or are willing to do:

We’ll see you tomorrow.
Perhaps dad will lend me the car.

We use would as the past tense of will:

• to talk about what people wanted to do or were willing to do:

We had a terrible night. The baby wouldn’t go to sleep. He kept waking up and crying.
Dad wouldn’t lend me the car, so we had to take the train.

• to talk about something that we did often in the past because we wanted to do it:

When they were children they used to spend their holidays at their grandmother’s at the seaside. They would get up early every morning and they’d have a quick breakfast then they would run across the road to the beach.

Conditionals:-

We use will in conditionals with if and unless to say what we think will happen in the future or present:

I’ll give her a call if I can find her number.
You won’t get in unless you have a ticket.

We use would to talk about hypotheses, about something which is possible but not real:

• to talk about the result or effect of a possible situation:

It would be very expensive to stay in a hotel.

• in conditionals with words like if and what if. In these sentences the main verb is usually in the past tense:

I would give her a call if I could find her number.
If I had the money I'd buy a new car.
You would lose weight if you took more exercise.
If he got a new job he would probably make more money.
What if he lost his job. What would happen then?

We use conditionals to give advice:

Dan will help you if you ask him.

Past tenses are more polite:

Dan would help you if you asked him.

Phrases with would:

• would you…, would you mind (not) -ing, for requests:

Would you carry this for me please?
Would you mind carrying this?
Would you mind not telling him that?

• would you like ...; would you like to ...,  for offers and invitations:

Would you like to come round to morrow?
Would you like another drink?

• I would like …; I’d like … (you)(to) ..., to say what we want or what we want to do:

I’d like that one please.
I’d like to go home now.

• I’d rather… (I would rather) to say what we prefer:

I’d rather have that one.
I’d rather go home now.

• I would think, I would imagine, I'd guess, to give an opinion when we are not sure or when we want to be polite:

It’s very difficult I would imagine.
I would think that’s the right answer.