In order to be a posek one must become a rabbi by obtaining smicha (rabbinic ordination) after the completion of an arduous learning program in Torah, Tanakh (Hebrew Bible), Mishnah and Talmud, Midrash, Jewish ethics and lore, the codes of Jewish law and responsa, theology and philosophy. Different denominations of Judaism have different requirements for becoming a rabbi; these are explained in the entry on Rabbis.
After becoming a rabbi one generally needs to become an expert in the responsa literature. The responsa literature consists of answers to questions that are asked to rabbis on all subjects; responsa (known in Hebrew as teshuvot) can be found in books, articles and even in personal short responses. The responsa literature has evolved greatly over the last millennium
Ultra-Orthodox Judaism has very strict requirements on who they consider to be a posek; Modern Orthodox Judaism and Conservative Judaism have what they hold to be more traditional requirements. Note that, as described in their respective entries, Modern Orthodox and Conservative Jews have different methodologies in how they approach Jewish law. Poseks are not found in Reform Judaism and in Reconstructionist Judaism, as these denominations do not hold that Jewish law is normative (i.e. to be accepted as binding.) Further, the Reconstructionist Rabbinical Seminary does not have a series of formal courses in Jewish law at all; they only offer a one semester overview on the subject. This is because Reconstructionist Judaism holds that Judaism is more of a culture than a religion, and thus precedent is gievn to studies of culture, song and history.