There are so many specific examples and idiomatic expressions that might require different explanations, but here are my general thoughts. Would isn't so much about the past, but rather about something possible in the future. It tells you that the action you are discussing depends on something else. "I would go if I had the time." "I would not talk to her unless she acts nicer." If "would" is combined with "have" then it refers to the past, but something that didn't happen. "I would have eaten more, but my stomach hurt." "They would have come, but their car was out of gas." Could can be the past of can, and it can also be a future/conditional form of can. "I could see the movie with you tonight if you could lend me some money." It is also used to make questions polite: "Could you help me?" Should implies that something is recommended, obligatory or necessary. "You should tie your shoes or you could trip and hurt yourself." "We shouldn't take pick those flowers. They might belong to someone!" Should, could, would--they are all auxiliar verbs that modify the meaning of another verb.

I get it. Thank you. :)

Generally we use "would" for kind request, "should" with advise and suggestion "could" for curious