The essence of converting to Judaism is to accept upon oneself the yoke of the Torah and its commandments before a rabbinic court. The potential convert is taught the fundamentals prior to conversion, and if he demonstrates a willingness to accept the yoke of the Torah, he is converted immediately and thereafter continues to study and grow as a Jew.
This practice has its source in a number of Talmudic anecdotes (Shabbat 31a).
Once, a non-Jew came before Shammai the Elder and said to him, “I wish to convert, but I will only do so on the condition that you teach me the entire Torah on one foot.” Shammai pushed him away, reasoning that it is impossible to teach a person the entire Torah on one foot. But the same individual came before Hillel the Elder, and Hillel agreed to convert him, saying, “That which is undesirable to you, do not do to your fellow. This is the entire Torah, the rest is all commentary.”
In other words, the idea that a person should not do to others that which he himself finds undesirable is the central idea of the Torah, and everything else is an expansion upon this idea, and in order to understand this you must continue studying.
On another occasion, a non-Jew came before Shammai and asked, “How many Torahs do you have?” “Two,” answered Shammai, “One that is written, and another which is oral.” The non-Jew said, “I can accept the written one, but I cannot accept the oral one. Convert me on the condition that you teach me only the written Torah.” Shammai scolded him and sent him away. He went to Hillel, and Hillel converted him. Hillel started teaching him and eventually convinced him to believe in the Oral Torah.
On one more occasion, there was a non-Jew who heard about the clothing of the High Priest and he became filled with the desire to become Jewish. He came before Shammai and said, “I would like you to convert me on the condition that I be able to wear the clothes of the High Priest.” Shammai immediately pushed him away, for it is well known that a convert cannot become a High Priest and hence is not allowed to wear his clothing. The same person approached Hillel and said to him, “I would like you to convert me on the condition that I be able to wear the clothes of the High Priest,” and Hillel accepted him and converted him.
The law says that if a non-Jew is not ready to accept upon himself all of the commandments, it is forbidden to convert him. How, then, did Hillel convert the non-Jew who only agreed to fulfill the written Torah? And how did Hillel accept the person who wished to convert on the condition that he be allowed to wear the clothes of the High Priest? After all, is it not forbidden for any non-Kohen, including a convert, to wear the clothes of the High Priest?
Hillel, in his great wisdom, understood that these non-Jews had pure and good intentions, and only lacked the ability to express themselves in a fitting manner. He was certain that when it came down to it, they would continue to learn Torah and fulfill all of the commandments (Tosafot, Yevamot 109b, s.v. Rah). From here we learn that it is unnecessary to learn all of the Torah’s laws before converting; it is sufficient that the rabbinic court reach the conclusion that the convert earnestly intends to join the Jewish people and accept upon himself the yoke of the Torah (Beit Yosef 268, end).
The sages teach (Shabbat 31a) that years later these three converts happened to be together in one place, and they said, “In his strictness, Shammai sought to drive us out of the world; in his humility, Hillel brought us under the wings of the Divine Presence.”
This is always a very difficult decision for a rabbinic court to reach. If, on the one hand, the prospective convert is sincere in his intention to keep the commandments but the rabbinic court suspects him of being insincere, the court causes great damage to both the Jewish people and the convert, and is punished for this. On the other hand, if the rabbinic court accepts somebody who does not intend to keep the commandments, it will cause great damage to the Jewish people.