At its core, conversion requires that the ger (convert) willingly, and without ulterior motive, accept kabbalat ol mitzvot - the acceptance of the mitzvot (commandments) upon him or herself. The classical sources say that, once this intent has been shown, he/she has to be taught a few "light" commandments and a few "heavy" commandments, and then they are ready to convert.
In modern times, this early stage has become quite involved. Although it varies greatly, based on the Rabbi, and the specifics of the case, conversion often takes a minimum of a year, and often quite longer. It involves education about the basic tenents and practices of Judaism, a chance to learn first-hand about Judaism by participating in Jewish life (one of the reasons for the year of study is to ensure that the ger has experienced all of the Jewish holidays, personally), as well as a chance to explore larger philosophical issues (such as theology) with the sponsorong Rabbi.
In Reform Judaism, there is also a major difference with the idea of kabbalat ol mitzvot. Unlike Orthodox and Conservative Judaism, Reform Judaism doesn't demand obedience of all Jewish laws; it instead insists on learning about those laws, and being guided by them. Most Reform Rabbis would insist on some serious level of observance before they would convert someone, but few would demand that any specific practices, such as keeping kosher, be adhered to.
The details of this preparatory period vary widely from movement to movement and, especially, from Rabbi to Rabbi. the only way to really get an idea of what is involved is to make an appointment with a Rabbi and ask him or her.
Once the candidate is ready for conversion, they are brought before a beit din, a Rabbinical court. This beit din ensures that the ger is ready for conversion (both in terms of sincerity, as well as general preparation for a Jewish life), and then (hopefully) accepts the ger ito the Jewish world. But, the ger is still not a Jew, at this point.
Once accepted by the beit din, the ger becomes a Jew by undergoing a ritual or two. Men are required to have a brit milah - a ritual circumcision. Men who were already medically circumcised instead go through hatafat dam brit - the ritual drawing of a drop of blood from the circumcision site. Both of these rituals officially bind the man to the brit (covenant) with God. The final stage of conversion, for men and women, is immersion in a mikvah - a ritual bath. Once that ritual is performed, the ger is now a Jew!
Again, in the Reform movement, standards vary. Some Rabbis insist on brit milah or hatafat dam brit and mikvah; some don't. The only way to be sure is to find a Rabbi, and ask!
Answered by: Rabbi Jason Rosenberg (Emeritus)