We use can to ask for and give permission. We use can’t to refuse permission.
‘Can I ask you something?’ ‘Yes, you can.’
‘Can I have some more potatoes?’ ‘No, I am afraid you can’t.’
You can go now if you want to.
You can have another piece of cake if you want to.
We can also use could to ask for permission. Note that could is more polite than can.
Could you help me?
Could I ask you something?
Could is not used to give or refuse permission.
‘Could I have a look at your papers?’ ‘Yes, of course, you can.’ (NOT Yes, of course, you could.)
May and might are also used to ask for and give permission. They are more formal than can and could. Some people think that may and might are more ‘correct’. However, in informal educated speech can and could are preferred.
‘Mummy, can I go to the movies?’ ‘No, you can’t.’ (Less formal than ‘Mummy, may I go to the movies?’)
‘Mummy, can I draw a picture on the wall?’ ‘You dare!’
Can and could are also used to talk about permission granted by rules and laws. May is not normally used to talk about rules and laws.
In most countries, you can vote if you are over 18. (NOT In most countries, you may vote if you are over 18.)