Errors abound (abundan) with these two words. Their uses are distinct.
“May” is about permission, or requesting something. It is polite and courteous. Contemplate these:
- May I read your newspaper?
- May I have another beer?
- May I sit here?
- May we study some English idioms?
Easy? Yes. “Can” is about ability or the capacity to do something. Consider these:
- Mr. Sanchez, the Spanish Prime Minister, can speak English.
- Jorge can ride a Ducati.
- Mr. Podemos cannot understand free markets.
So, if someone says to you, “can I read your newspaper”, you will be confused. There are two options. The first option is that he really means “may I read the newspaper”.
The second option is that he is asking himself (preguntándose) whether or not (si o no) he has the ability to read it. Then why is he asking you that question, when he should know the answer? Who knows?