This question gets asked a lot. "Could" means that you are able to do something; "would" means that you want to do it. "Could you lift 50 kilos?" "Yes, but I wouldn't. It's too much work, even though I could." If you're asking somebody to do something for you, you would use "would". "Would you please get me the hammer in the next room?"

Could indicates capacity to do things. I could eat lots of food. Would entails that there's an intention to do the task (in the future). I would sing in the contest tomorrow.