How and what should the Buddhist believe?

The Buddha is the Enlightened One who discovered the Supreme Truth. He did not force anyone to believe in His teaching with blind faith. The reasonableness of the Dhamma, the Buddha’s teaching, lies in the fact that it welcomes any critical examination at all stages of the path to enlightenment. To understand the nature of all phenomena, insight wisdom must be operative throughout.

 Once the Buddha has instructed the Kalamas, who were inhabitants of Kesaputta, a town in the kingdom of Kosala, on an appropriate attitude towards the religious beliefs. He said
“Do not accept anything on mere hearsay, nor by mere tradition, nor on account of rumours, nor just because it accords with your scriptures, nor by mere suppositions, nor by mere inference, nor by merely considering the appearances,nor merely because it agrees with your preconceived notions, nor merely because it seems acceptable, nor thinking that the recluse is our teacher.”

And then the Buddha had further instructed the Kalamas to consider everything by themselves carefully. He said

“When you yourselves know that these things are bad; these things are these things are blamable; these things are censured by the wise; undertaken and observed; these things lead to harm and ill; abandon them. And in contradiction, when you yourselves know that these things are good; these things are not blamable; these things are praised by the wise; these things, undertaken and observed, lead to benefit and happiness, enter on and abide in them.”
[Kalamasutta]