1. PERMISSION
CAN
We can use « can » to ask for permission to do something.

e.g.
Can you put some music on ?
Can I see my friends ?
Can we eat now ?

COULD (not to be confused with could in the past simple)
« Could » is more formal and polite than « Can »

e.g.
Could I have a dog for my birthday please ?
Could I come to the party with you ?
Could I go out tonight ?

2. DEMAND
COULD YOU
Tell or ask someone to do something for you.

e.g.
Could you give me a menu ?
Could you be quiet ?
Could you driver slower ?

3. OFFERS
CAN I
Offers of help

e.g.
Can I help you ?
Can I do that for you ?