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.
To become a true Buddhist one should have a pleasant mind towards, and confidence, in the Supreme Buddha. This confidence should be rooted (mulajata), and it should be well established (patitthita). To develop this kind of unshakeable confidence, it is important to know about the knowledge of The Buddha. A “Sotāpanna”/stream entry Buddist is a True Buddhist.

The Pali Canon recognizes four levels of Awakening, the first of which is called “Sotāpanna”/stream entry. This gains its name from the fact that a person who has attained this level has entered the "stream" flowing inevitably to nibbana. He/she is guaranteed to achieve full awakening within seven lifetimes at most, and in the interim will not be reborn in any of the lower realms.

The practices leading to stream entry are encapsulated in four factors:  

Association with people of integrity is a factor for stream entry.  

Listening to the true Dhamma is a factor for stream entry.  

Appropriate attention is a factor for stream entry.  

Practice in accordance with the Dhamma is a factor for stream entry. 

The Sotapanna is free from the following three fetters (samyojana):– 

1. The wrong view that the aggregates of physical and mental phenomena are ego or self. (sakkāya-ditthi or personality-belief).
2. Any doubt about the Buddha, the Dhamma, the Sangha and the discipline (vicikicchā or sceptical doubt).
3. Belief that methods other than that of cultivating the qualities of the eightfold noble path and developing insight into the four noble truths will bring eternal peace (silabbataparāmāsa or belief in mere rite and ritual).

Furthermore, his observation of the five precepts remains pure and absolute, as a matter of course. For these reasons a Sotāpanna is well secured from being reborn in the unhappy existences of the four lower worlds. He will lead the happy life in the world of human beings and devas for seven existences at the most and during this period he will attain Arahantship and nibbāna.

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