Jew is usually someone born of a Jewish mother (but in very liberal cases, a paternal line is sometimes acknowledged today).
Interestingly enough, in Bible times a Jewish identity was reckoned from the male line and only after the founding of Rabbinic Judaism did it change to the maternal line (it's thought around the 4th or 5th century C.E. although no one knows for sure). It's funny because I always assumed it had always been through the female line, since back then it was the only provable line.