What's the path to becoming a Jewish Orthodox Posek (like R' Yechiel Michel Epstein, a.k.a the Aruch Hashulchan). What Sefarim does one have to learn? What learning method is the most effective?
According to the Gemara in Sanhedrin (5a), one would need to be learned (גמירנא), able to reason (סבירנא), and have permission from his (qualified) Rav (נקיטנא רשותא). Normally, a rav will only grant this permission, known (colloquially) as סמיכה, semicha, after being satisfied that the student has proven the first two conditions, and possibly after an internship period known as שימוש (shimush).
There are several different areas of Rabbinic expertise. For most religious questions (איסור והיתר), the permission is referred to as יורה יורה, "He may teach" (or decide). For religious civil law, the permission is called ידין ידין, "He may judge" (or adjudicate). Semicha may be limited to the scope of an individual's areas of knowledge (e.g. Shabbos, kashrus, Nidda) within the Shulchan Aruch.
There are many Kolels with semicha programs, and I believe Yeshiva University has one as well. These programs generally focus on Orach Chaim, the laws of Shabbos and Yom Tov (sections 2 and 3, or 3 to 6 in the Mishna Berura), and on Yoreh Deah, the laws of kashrus (בשר בחלב and תערובות) and purity (Nidda and tevilla). Other programs focus on civil law (in Choshen Mishpat) or on marital law (in Even HaEzer). Those aiming for pulpits (or community rabbis) may have more specific requirements.
As for authoring a sefer, I would suggest that the question is a bit premature. (Especially if you're asking on this site.) However, the upper echelon of Poskim can generally issue rulings in all four sections of the Shulchan Aruch, and amass enough experience to gain acclaim among their colleagues others so they become the targets of queries (שאלות). Eventually, an especially accomplished posek may have enough responses to be able to publish a sefer of שאלות ותשובות (Responsa). Others may be able to write a commentary, or clarify a section of laws in their own words. Aruch HaShulchan is of this latter form, and was written after Rabbi Epstein had been the rabbi of a large community for a number of years.