Question: In this society a lot of people say "I'm a Buddhist" but they're just saying that. So my question is, how can a person become a real Buddhist? And how do we know he's a real Buddhist?

Answer: 
You become a real Buddhist when you walk the path of Dhamma. The Buddhist teaching is to be experienced here and now and to be verified here and now. There are many ways this has been put forward:

* Sila - Samadhi - Panna where later is realisation at the experiential level or at the level of wisdom
* Pariyatti - Patipatti - Pativedha where the latter is the experience
* sutta-maya-panna - cinta-maya-panna - bhavana-maya panna where the latter is experiential wisdom

When you have the 1st vision of the Dhamma your faith never changes. This is because nobody can convince you otherwise of what you have already seen for yourself.
I think a real Buddhist at the very least follows the five precepts.