We often use would not to talk about past refusals:
• He wanted a divorce but his wife would not agree.
We sometimes use would (rather like used to) when talking about habitual past behaviour:
• Every weekday my father would come home from work at 6pm and watch TV.
would games for past habit
would for the future in past
When talking about the past we can use would to express something that has not happened at the time we are talking about:
• In London she met the man that she would one day marry.
would for conditionals
We often use would to express the so-called second and third conditionals:
• If he lost his job he would have no money.
Using the same conditional structure, we often use would when giving advice:
• I wouldn't eat that if I were you.
Sometimes the condition is "understood" and there does not have to be an "if" clause:
• Someone who liked John would probably love John's father. (If someone liked John they would probably love John's father.)
would for desire or inclination
• I'd love to live here.
would for polite requests and questions
• Would you open the door, please? (more polite than: Open the door, please.)
would for opinion or hope
• I would imagine that they'll buy a new one.
would for wish
• I wish you would stay. (I really want you to stay. I hope you will stay.)
would for presumption or expectation
• That would be Jo calling. I'll answer it.
would for uncertainty
• He would seem to be getting better. (less certain than: He seems to be getting better.)
would for derogatory comment
• They would say that, wouldn't they?
would that for regret (poetic/rare)
This rare, poetic or literary use of would does not have the normal structure:
• Would that it were true! (If only it were true! We wish that it were true!)