As a native English speaker, I don't know the rules; I just know what sounds correct. If you want to practice, you could try quizzing yourself here: http://www.englishpage.com/modals/interactivemodal6.htm . I will try to summarize the rules for using both of these words. I am copying from http://en.wikipedia.org/wiki/English_modal_auxiliary_verb . Deciding which is appropriate depends on both grammar and context. I'll list and explain some examples in another post—I'm up against the character limit. 'Could' can often replace 'can', although generally it gives the phrase a conditional tone. 'Could' functions as a kind of past tense for 'can,' though 'could' does not function grammatically like any regular past simple verb. ‘Could' carries the same meaning as 'might' or 'may' in the present—it suggests something is a possibility. 'Would' is originally the past tense of 'will', and it is still used in that sense. Its more common use, however, is to convey the conditional mood, especially in counterfactual conditionals; that is, to express what would be the case if something were different. 'Would' can also be used with no modal or temporal meaning, to affect either politeness or formality of speech.

Both are used in questions, as a request. 'Could' is more cautious, often used when the other person does not know what you want him/her to do. Generally both can be used in the same context.

hi can and could are often interchangeable for the same function and tense. there is a slight distinction in meaning btw these two modals in those cases for examples: I can arrive at the reception early to make additional arrangements. I could arrive ............arrangements . so both of these exp express possibility in the future but in the first exp the use of can expresses a slightly more definite possibility. i could speak spanish when i was a child . means ability in the past And would also it is a modal that expresses polite request exp : i would like a cup of tea, please or it can expresses simply unreal in the past means conditional exp: if i were you i would change my behaviour or if john had studied more, he would have got better marks. means unreal in the past . hope this will help you

Here's some examples "I could help you with your work" gives a tentative sense of ability to help. There might be an implicit conditional by using 'could' in this sentence instead of 'can'. Using 'would' in this case would give the sentence a sense that there might be something preventing you from helping. I think it would sound funny to use 'would' and not continue the sentence. "John is not in the office today, he could be sick." In this case, it would not make sense to use 'would' because the sentence expresses a possibility. "In the 1960s, people thought we would all be driving hovercars by the year 2000." In this case, using ‘would’ implies that people were certain. Using 'could' in this case would indicate they thought there was only a chance people would all be driving hovercars. "I would like a glass of water, please." In this case, it would not make sense to substitute 'could'. I could leave. In this case, the speaker is making a suggestion and it wouldn’t make sense to use 'would'.