If you notice that a co-worker is rude to customers, what would you do?

That depends whether my job is commission based or not. If it is commission based, then I would be glad. I would be extra caring to customers so that they would choose to approach me rather than him. That means extra income for me. LOL. However, if it is not commission based and we get the same salary, then I would talk to him and help him if I can. If it is beyond my capability, then I would ask someone who could.

Explain to him about the repercussions of being rude to a customer.  

I will try talk to him and advice him to be professional because being polite with customers is most important role in customer care. In the end if he didn't change his behaviour I will notes him that I will report him to the manager.

1. Will speak to him and suggest him the right way to deal with the customers

I Will try to convince the customer at any cost and later I will have a discussion with my friend, will be requesting him not to be rude to the customers as they are the ASSET of the company. And also Ill watch him closely, so that if he repeats the same anytime ill help him how to handle that situation. 

Try to talk to him/her. Also alarm your supervisor. He/She may be having frustrated with his/her life and a bit of personal, friendly advice might be helpful.

1. Speak to them privately
2. Find out the reason for being rude
3. If they continue to be rude with customers, I will report them to the manage.

Will advise him edit his behavior with customers

the answer is simple, that is why it is recommended to have a  HR department in companies who are supposed to train people for that or when such problems appear should talk with co-worker.

Basically the role of a customer care representative is to be cordial and polite with the customers.  However, If a situation arises where a co-worker is being rude to a customer, in that case, I would step in and take over the situation and tell my colleague to go out of sight for a while and at then apologize to the customer for my co-workers rudeness on behalf of the organization.  Carry on from there.