Answer:
   
   Jewish tradition dates itself back to Sinai. In other words, "the
   Torah" that the Jews recieved in the desert includes not only the text
   of the Five Books, but also a vast body of what we generally call Oral
   Torah. This means that the laws of conversion, or at least, the
   principles from which they derive, are as old as the Torah.
   
   Before the covenant at Sinai, there wasn't really Judaism per se. One
   could join the earlier covenant that G-d made with Abraham, but there
   could be no parallel to the conversion of today. The forefathers'
   wives therefore didn't need to formally convert. And, depending upon
   the sequence of events, if Jethro became a Jew before the revelation
   at Mount Sinai (which is the order the stories are told in the text)
   he didn't have to formally convert either.
   
   We do find that the Israelites who left Egypt were taken through the
   same steps that a convert would take today: the men were obligated to
   circumcise themselves before leaving Egypt, they immersed themselves
   three days before the revelation, and they were formally asked if they
   would accept the yoke of observance the day before recieving the
   decalogue. The Talmud find allusions in the book of Ruth that indicate
   that she converted according to the current process. The same word,
   "geir", is used in the Torah to describe two kinds of people. As this
   causes confusion, the Talmud utilizes adjectives to distinguish the
   two. The "geir tzedek" (righteous convert) is what we usually think of
   when we say "geir". However, there is also the person who decides to
   observe the 7 categories of laws required by G-d's covenant with Noah.
   In modern parlance such a person is called a "Noachide" (or Noahide).
   
   How does this relate to "geir"? Here's how. A Noachide who agrees to
   live in a Jewish Israel, within a government run by Torah law (such as
   that of the 1st Temple period, or under the Sanhedrin, or after the
   messiah establishes a third commonwealth), but as a non-Jew is called
   a "geir toshav" (a resident alien). A geir toshav only goes to court
   (which can be any three observant Jewish men of sound mind) and
   proclaims his/her acceptance. Because of the ambiguity of the term
   "geir", people reject our beliefs about the origins of the Oral Torah
   assume the two, geir tzedek and geir toshav, are identical. This would
   make it seem that the text is only obligating a proclamation of
   acceptance. This, however, leads to inconsistancies. On the one hand,
   "one law shall you have for yourselves, for the geir and for the
   native of the land". Including rituals. This expression is used
   (amongst other places) in discussing fasting on Yom Kippur, where the
   punishment is phrased as "he will be cut off from amongst his people,
   Israel". So, this geir is a member of Israel. However, the word "geir"
   as used in a verse about working on the Sabbath does not assume that
   when G-d speaks to Israel, the geir is included. "Do not do any work,
   [neither] you, your son, your daughter, your servant, your
   maid-servant, your animal, and the geir who is within your gates." The
   geir isn't included amongst the "you". There are numerous examples of
   each side of this dilemma.