Can is a modal verb which denotes ability to do something and maybe replaced by to be able to.
Ex. I can do it. I am able to do it.
It also may mean a permition to do something.
Ex. You can go home now.
Ex. You cannot go outside unless I permit you.
In negative sentences it may also mean a strong level of doubt
Ex. She can't be at home now.
In interrogative sentenses it may express surprise
Ex. Can he still be working here?
or a request to do something
Ex. Can you do me a favour?
Could expresses all the same as can but in the past tense. NB Could is used to express polite and/or formal request
Ex. Could you do me a favour.
Would is a form of will used in past tenses and has the same meanings. NB would is also maybe used to express polite and/or formal request
Ex. Would you do me a favour?