A Jew is one who follows Judaism, a monotheistic religion. Generally, Judaism (and, by extension, a Jew) believes that: G-d exists; G-d is one and unique; G-d is incorporeal; G-d is eternal; Prayer is to be directed to G-d alone and to no other; the words of the prophets are true; Moses' prophecies are true and Moses was the greatest of the prophets; the Written Torah (first 5 books of the Bible known as the Chumash) and Oral Torah (teachings now contained in the Mishnah, discuessed in the Talmud and other writings) were given to Moses; there will be no other Torah; G-d knows the thoughts and deeds of men; G-d will reward the good and punish the wicked; the Messiah will come; and the dead will be resurrected.
According to Halacha (pron. "halakha" - Jewish religious law) children of Jewish mothers and those who have converted to Judaism are considered Jews. The denominations of Judaism in the United States are Orthodox, Conservative, Reform, Reconstructionist, and Humanist. They differ as to the requirements for conversion and whether descent is through the mother (the traditional position adhered to by the Conservative and Orthodox movements) or may be through either parent (the Reform and Reconstructionist position). Although one need not practice Judaism to be accepted as a Jew, Jews generally consider a convert to another religion as no longer being Jewish.