Who is a Jew?

Ran into this web site called Being Jewish while checking on something completely different than what I was looking for (doesn't that always happen?) where this statement was made: "The Torah also forbids a Jewish man to marry a Gentile woman, and if he does, his children by that woman will not be Jewish."

Having my curiosity pricked I decided to write and ask a question. My question was: How do you explain Boaz's marriage to Ruth?

As you will recall Ruth was a Moabitess. She later was married to Boaz, a Jew (Ruth 4:13). Thus springing from Boaz's loins came Obed who was the grandfather of David who later became the King of Judea (Ruth 4:17).

When, or if, I get an answer I'll fill you in.