Belief can come from a personal revelation. A good friend of mine was planning to commit suicide on our way home from school in 10th grade. He asked of God that a particular song on play next on the radio if God cared and did not want him to kill himself, and that song came on.
Belief can come from instinctive conviction and commitment. This past year a good friend and I carpooled with a very smart, very skeptical Jew, who very methodically and academically ripped any rational argument for judaism to shreds, and called in to question the whole validity of the Torah. My friend had a serious crisis of faith after one ride. God suddenly be came a demiurge, an opiate of the masses, and a passing fantasy in man's search for meaning, alongside his Omnipresent self. He began to cry, and swore with God's name, and heaven and earth as his witnesses that he would be a jew and uphold Judaism were he the last jew a live, standing before a firing squad, who would spare him if he forsook Judaism, in the face of undeniable evidence of its fallaciousness.
Belief can be a rational choice, based on experience. One can choose choose Judaism because, having studied the Torah they cannot deny that it improves my life and character, and they feel that the set of rules it lays out for mankind, if properly enforced, would do the same for the world.