If you can trace a pure matralinear line from your mother, even if it's more than 10 generations, you are a Jew.
Judaism is a very technical religion. When gestating, you are a part of your mother. If she is Jewish, you are Jewish, once born, if you were Jewish while gestating, then you are now Jewish. If not, then you can convert but are not a Jew-by-birth.
While Judaism is not a proslytizing religion, we will welcome converts. We don't believe that only Jews make it into heaven and therefore don't belive that conversion to Judaism saves everyone from "hell". We believe tha any non-Jew who lives by the Noahide Laws (there are plenty of sites where you can find these and I don't want to fill up space repeating them here) will get into heaven and encourage those who are not Jewish to live moral lives and those who are already Jews to live by the full set of laws that apply to Jews.