How can someone become Jewish?

Since Jews do not actively seek converts, the process begins when someone approaches a rabbi or teacher and says that they have the desire to convert to Judaism.  Traditional Jews (Orthodox) will usually discourage them from doing so and only after they come back with this request and are turned away at least two times, then they may be considered sufficiently serious about this matter.
In liberal Jewish movements, however, this request is usually answered in the positive on the first time. In all cases, the prospective convert goes through a period of intense study of at least 9 months with a rabbi or scholar to learn about Jewish practices, Bible, history, holidays, prayers, ethics, philosophy, and lifecycle – and perhaps learning to read basic Hebrew.
It is a time for deep reflection and questioning so that both the convert and his/her teacher feel truly ready to take on this new life since being Jewish is not just about taking on a new faith, but also becoming part of an ancient people who have a rich culture that continues to develop in every generation.
As such, they are also asked during this time to begin practicing Judaism by attending prayer services at the synagogue, by observing the Sabbath and Jewish holidays, by participating in events and social action work in the Jewish community, and acquainting themselves with Jewish organizations and Jewish literary resources.
The prospective convert then goes before a rabbinic court – called a Beit Din – which consists of three ordained clergy; they question him/her about what they have learned and what has brought them to this decision.  While many come to this because they have fallen in love with someone Jewish and want to get married, the court does not consider this a sufficient reason because one does not know if a marriage will last, and this is something that must be taken on fully because the individual wants this regardless of any extenuating circumstances.
Following the questioning by the court, there is the ceremony of immersion in a ” mikveh” – a body of free-flowing, fresh water. Today this is usually done indoors in specially constructed small pools, kept immaculately clean, and usually about 4 feet deep.  All clothes, jewelry, accessories,  and makeup must be removed so that all parts of the person’s body can be touched by the water. The person immerses totally, with head under, three times, while reciting special blessings when he/she emerges on two of the times. A member of the Bet Din who is of the same sex as the convert witnesses this and may assist with the recital of the prayers.  Family and friends greet the convert after this and a often a special certificate is given at this time, with the new Hebrew name that the convert has chosen.
Also, on the Sabbath morning following the immersion ceremony, the convert is called up to the Torah using their new Hebrew name, blessings are said over him/her, and the honor of blessing the Torah scroll  or carrying the Torah is given to the convert; many times there is also a small party in their honor at the reception following the Sabbath morning services.  Once a person has converted to Judaism, they are to be recognized, welcomed and accepted by the community as no different from someone who was born Jewish.
Thank you to Rabbi Dorit Edut