Which Sefer or Sefarim is/are used in practical application of Shechita? General Halacha follows the שלחן ערוך, but does it in all areas?
In America, the custom is as the custom of Europe -- to use the sefer שמלה חדשה, written by Rabbi Alexander Sender Schor (1673-1737), even though on occasion he will disagree with the שלחן ערוך. Rabbi Schor also wrote תבואת שור (an explanation to Simlah Chadasha) and בכור שור, a commentary on Shas.
(see מטה אשר [commentary to שמלה חדשה] in 1:4, especially what he quotes from the דרכי תשובה)
I had heard that the custom in Israel is to use the בית דוד, though some commenters on this answer had heard otherwise.
If you wish to get tested by the Chief Rabbinate of Israel you must be proficient in Tur, Shulchan Aruch with Nosei Kelim.
Rabbi Chaim Lokie in his English Simlah Chadasha (footnote Siman 18) writes that many in Israel are accustomed in the learning of Sefer Beis Dovid. Rabbi Yehudah Landsman of Monsey would also teach Beis Dovid to his students.
Many in the United States - like Moreinu Rav Eliyahu Ben-Chaim of Yeshiva University - allow you to learn any Sefer that is accepted by Gedolei Yisroel (Tur Shulchan Aruch, Simlah Chadasha, Beis Dovid, etc.).