What are the essential requirements of conversion to Judaism, such that if one of these requirements is not fulfilled the conversion is invalid?
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Someone wishing to convert will work with a rabbi, who will guide the convert through the process and ensure that the following requirements are met before proceeding to the beit din (court).
A convert, first and foremost, must accept the yoke of the mitzvot (kabbalat ol mitzvot). In other words, a convert must be doing it out of a sincere desire to join the Jewish people and take on its responsibilities. Rabbis will initially discourage converts.
Some course of learning will be required. From what I understand, this is a combination of nuts and bolts (b'rachot, t'filah, shabbat, kashrut, some Hebrew, etc), Tanakh, history, and theology. Once someone converts he becomes liable for transgressing mitzvot, so he needs to know how to live as a Jew first. In the US today this learning tends to be a combination of classroom study and individual study with a rabbi.
Some lifestyle changes may be necessary, ranging from replacing kitchen utensils and kashering to changing work schedules to, possibly, moving into an observant community within walking distance of the shul. The rabbi working with the convert will provide guidance here.
The ritual requirements are (per R. Maurice Lamm, Becoming a Jew, p119):
When the temple stands, the convert is also liable for a korban (offering).
My understanding is that once a conversion is done by a qualified beit din, it stands even if something happens to call the convert's motives into question. If it turns out that the beit din was not qualified, I'm not sure what happens -- I think there is disagreement.
1 R. Lamm (p133) says that one of the three must be a rabbi, and that rabbi chooses two other knowledgeable and observant men.
(And add an animal sacrifice, back when those were doable.)