The answer begins not with the process or place, but with your status.
If you are not Jewish, or are affiliated in any way with another faith or religion, you cannot be ordained as a rabbi, period.
If you are Jewish by birth, or have undergone a formal conversion process led by a recognized rabbi, then you may be eligible to begin the effort to undertake the process.
Only at this point would your gender enter into the matter. The Orthodox movement does not permit the ordination of women as rabbis (though recently one Orthodox rabbi ordained a woman with a different title than rabbi; it is not certain that this situation will stand, nor is it clear that it will be accepted in general in the Orthodox world). For purposes of this answer, we will exclude the Orthodox movement as a possibility for you.
The next step is that you would apply to the appropriate seminary as a graduate student, including your GRE scores, transcripts, essays, and other information. You might be asked to take a psychological evaluation at this point. If you have the appropriate credentials, you would be granted an interview with the admissions committee. Your application would then be evaluated, and a decision made. Assuming you were accepted, you then attend seminary for the next five or six years.
There are seminaries for the Reform movement in New York, Cincinatti, Los Angeles, and Israel; for the Conservative movement in New York, Los Angeles, and Israel; for the Reconstructionist movement in Philadelphia. In all of these programs, all students are required (in general) to spend a year studying in Israel.
Upon completion of the academic requirements, the faculty of the institution would determine the fitness of the candidate to serve as a rabbi. If they felt that a person was not suitable, they would grant them a degree, but not ordain that person. Ordination coincides with graduation for most candidates.
In some instances, more often in Europe than the US, there was a process of ordination following apprenticeship. This model is followed somewhat today within the Jewish Renewal movement. It requires studying, working, and apprenticing with an ordained rabbi who serves as your primary teacher and mentor, and then as your sponsor, presenting you when ready to the rabbinic court that tests you and determines your knowledge, readiness, and suitability to be ordained.
There are other seminaries that have been developed in the last few years. These are not associated with a particular movement, but there is no guarantee that any particular movement will recognize their authority to grant ordination or to train rabbis.
Specific details may differ, but this is a general outline.
In Orthodoxy, there really is nowhere. Harsh as that sounds, and I apologize for it, it stems from Orthodoxy's continuing awareness that men and women are inherently different in certain ways. We all recognize that truth, but in Western society, we insist the determination of the ramifications of those differences rest solely with the individual. While to a large extent it does in Judaism as well, God in the Torah and our Sages in their transmission of that Torah made clear certain parameters for those differences that cannot be crossed; that is proably because Judaism recognizes that we are not only individuals, we are also members of communities, and, as such, our actions as individuals also deeply affect our communities. That being true, the community has the right, even responsibility, to give guidance as to the limits of propriety in many areas of life.
What is more accepted, and I believe a more productive avenue to follow, is finding roles for women that allow them to exert the positive influence for which they yearn. Women across Orthodoxy are regularly trained to be, and accepted as, educators in schools at all levels and in adult education programs; women in various capacities visit the sick, comfort the bereaved, clothe the naked, counsel the troubled, all the kinds of activities that have become attached in our minds (but not in Judaism's conception of the position) to the role of a rabbi. All of these, for large parts of the Orthodox world, are as available to women as to men. To get trained to perform those functions, a woman can train in Israel at places like MaTaN and Nishmat, at Yeshiva University's Stern College for Women and related graduate schools, and probably at many other institutions besides.
For a woman who is insistent on achieving the title "rabbi," there are the other denominations of Judaism, Conservative, Reform, etc.
Ordination as a rabbi within any denomination is a long, arduous but rewarding process of study, practice and reflection. There are several options as a woman as to where to go. However, the first step in your process is determining where you fit, if at all, on the denominational spectrum. Each movement has clearly held beliefs, philosophies and ideas about Jewish life and thought. It is important to explore where you fall in the spectrum to determine what the right school for you. Most of the schools have a 5-6 year process of graduate school often incorporated with work in the field. The movement, where I was ordained is the one I can share the most about but here are some basics on all the options.
The Conservative movement ordains rabbis in 3 places: Israel, NY and Los Angeles.
The school in Israel: Machon Shechter can be found here...http://www.schechter.edu/Page.aspx?ID=993608081
The school in NYC: The Jewish Theological Seminary can be found here http://www.jtsa.edu/x731.xml
The west coast school is Los Angeles: The Ziegler School of Rabbinic Studies at the American Jewish University can be found here: http://www.ajula.edu/Content/ContentUnit.asp?CID=187&u=982
Independent: The Hebrew College in Boston and the Academy of Jewish Religion in NYC and Los Angeles, all ordain women and men independent of any movement affiliation.
Reform: The Reform movement also ordains women at its Seminary - Hebrew Union College, Institute of Jewish Religion (HUC-JIR) on campuses in Cincinnati, NY and Los Angeles.
Reconstructionist: This movement ordains its rabbis in Pennslyvania at their seminary the Reconstructionist Rabbinical College.
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