The modal auxiliaries "would" and "could" are important, as they help you to be polite and diplomatic when you speak or write English.
This is especially useful when you want something from another person, or in certain situations where being diplomatic is important, such as in a negotiation, or when you are speaking to someone in authority (such as your boss!)
Would
We use "would" to talk about hypothetical situations, not facts. Using "would" helps to put a distance between us and the other person.
You can use "would" to replace "will", "want" and the verb to be.
For example, rather than saying "That is a problem", say "That would be a problem". (i.e. it would be a hypothetical problem.)
Rather than "I want a bigger discount", say "I would like a bigger discount".
Could
We use "could" instead of "can" to be polite. Remember: often in English past forms are more polite than present forms, because they create a distance. (i.e. they are further back in time, rather than being in the present.)
You can use "could" to replace "can" or to talk about possibility, ability and permission.
For example, rather than saying "Can I interrupt?", say "Could I interrupt?"
Instead of saying "What discount are you going to offer?", say "What discount could you offer?"