There are two ways someone can be a Jew. You can either be born a Jew or you can convert. Being born a Jew is pretty simple. It doesn t matter whether your father is Jewish or not.
Conversion is much more complicated.
Judaism does not actively encourage conversion, in fact, to a large degree it actually discourages it. This is the reason Jews have never had missionaries trying to convert non-Jews. This does not mean, however, that Judaism doesn t want the convert. Discouraging conversion helps to filter out those lacking the proper degree of commitment. If any such intent is found the court may not accept him or her for conversion.