People believed him because when you are the one in charge of a big country and tell lies over and over again, people will start to believe you. Germans were brainwashed to believe his lies.
After WW1, all of the blame was placed on Germany, so their economy went down hill. So, when Hitler came to power, he deemed Jewish people responsible for whatever reason. Hitler saw Jews as less than people, had a very strong hatred, and is generally just a bad person, so that's why he choose them as his Target instead of asking them to leave.