How can Mormons think what they believe is true?

It's just like every other religion out there. He just found a lot of people who he managed to convince into believing what he said. You must also remember that the times he lived in were still very religious. A lot of people probably thought "Oh, hey, I agree that so-and-so is wrong and I agree that such-and-such is a God given right!" and after that he just manipulated into believing everything else.