Can I? Could I? or May I?  Can you? Could you?

When you ask for permission or a favor:

In informal situations you can use 'can'.
In semi formal situations you could use 'Could'
In formal situations and if you want to sound polite, you may use 'may'.

For example,
To your brother

Can you drive me to the railway station this afternoon?
Can you turn off the TV?
To the waiter
Could you bring me a glass of water?
Could you direct me to the elevators please?
The clerk to a customer
May I help you?
May I help you carry your bags sir?
To the boss who is very strict
May I take the day off on Friday? I need to take my mother to the hospital.

Can and Could can be used with all the pronouns (I, we, you, he, she, it, they, etc.)

May is used with I or we only

Can/Could/May I have some tea?
May I leave?