We could discuss what makes someone a Jew for ages, but a bottom line is that it isn't simply about belief the way it is for other religions. A person can certainly convert, but it often involves a complete lifestyle change (dress, eating etc) and participation on rituals that can take months or years to complete. For this reason, one of my professors told me that people who inquire about conversion are often turned away at first to ensure that the person fully understands what they're getting into. When you consider how many people adopt things just because X Celebrity does it, it makes perfect sense.
Jewish heritage is passed down through the mother, not the father. If your mom is Jewish, so are you. In this sense, belief and action have nothing to do with it. However, a Jew who has converted to another religion is seen to have "left the family". “Family” is probably a more accurate descriptor than “nation” or “race” because it refers to the way Jews with different customs or from different parts of the world still feel a sense of unity.
While some believe it begins earlier, Judaism views birth as being the beginning of life, not conception as many Christians do. If carrying a pregnancy to term will endanger the mother's life, she is encouraged (some say required) to terminate the pregnancy. That might sound callous to some, but it's important to remember that the fetus is considered a potential life, not a full life as many Christians teach.
I found it interesting to learn that any Jewish person who has not adopted another religion (see "heritage" comment above) can emigrate to Israel and immediately be considered a citizen.
For purposes of observance, the Jewish calendar views days as beginning at sundown. The Sabbath, the day of rest, begins Friday evening and ends Saturday evening.
Since their calendar is lunar rather than solar, Jewish holidays fall on different days each year. Also, holidays technically start on the night before the day appears on the secular calendar. For instance, a holiday noted on August 24 on the calendar actually begins at sundown August 23. For a further explanation of holidays, visit http://www.jewfaq.org/holidayg.htm.
“Kosher” or “kashrut” are words used to describe the dietary and food preparation laws Jews live by. One thing I found particularly interesting is that consuming blood of any kind is forbidden for the same reason some groups refuse blood transfusions-blood is considered to be the “life” or “soul” of a creature. I won't go into detail about the method, but there are strict instructions on how an animal is to be slaughtered to ensure that it suffers no more than it absolutely has to. If you ever have steak at a kosher steakhouse, you may find that it is not as tender as non-kosher steaks because non-kosher steaks come from a part of the animal (mostly toward the back) that contains the sciatic nerve and blood vessels. If you've ever seen the Hebrew National commercial that says they use “no ifs, ands or butts”, this is what they're referring to. While this non-kosher nerve can technically be removed from the meat, it's a very difficult and expensive process a lot of kosher butchers don't go through.
For more information regarding “kosher” or “kashrut”, see http://www.jewfaq.org/kashrut.htm.
This is just the tip of the iceberg, so consult http://www.jewfaq.org/index.shtml or http://www.beliefnet.com/Faiths/Judaism/index.aspx for more information.