The typical requirements are an accredited bachelors degree (though in some cases, an equivalent can do) and whatever courses they list in their list of admissions requirement (for medical schools it is very set, for business and law its whatever catches the fancy of the admissions officers, for most non-professional graduate programs it is the equivalent of a BA major program in the subject). Then there are the standardized exams such as the LSAT.
Once you meet the minimum requirements, the trick is to convince the admissions officer that you are interesting. Some programs have essays and interviews. You have to convince them your background is a good fit for their program. It is actually quite subjective.
Also remember that the prestige of a school doesn’t necessarily correlate with employability. If your goal is to be a lawyer in the frum community (i.e. a small firm in Boro Park), a degree from Harvard or Columbia may be less valuable than one from a lower ranked school that specializes in preparing students to practice in Brooklyn rather than working for “Big law.”