The Rambam's own description of tying is that one winds a white strand once, then the techelet strand twice, ties a knot, and repeats this pattern of windings separated by knots until the final section (Mishneh Torah, Fringes 1:7-9), building on his opening specification of how the eight strands are inserted and measured (Mishneh Torah, Fringes 1:6). The Arukh HaShulchan notes that the Rambam does not require the strands to be twisted (שזור) at all, citing the Rambam's own language that twisting is optional and that even an eightfold twisted strand counts as one (Arukh HaShulchan, Orach Chaim 11:1-25). Rav Schachter's sheet brings the Bach's reading of the Rambam's structure, explaining that the Rambam first states the law for when techelet existed and only afterward returns to the practice that applies even absent techelet, including the winding of the long strand around the seven (Bach, Orach Chayim 11:1-3). The Rambam's own responsum addresses a questioner's confusion over his count of threads and windings, explaining that one should spin a single strand partly techelet and partly white, inserting and doubling each thread so that seven strands are white and one techelet, since the pasuk speaks of a single petil techelet (Teshuvot HaRambam 28:1-2).
The Shulchan Arukh records the more common practice of tying five double knots with four intervening sections of winding, with the Rema adding the custom, attributed to the Rambam's method, of winding seven, eight, eleven, and thirteen times in the four sections, totaling thirty-nine plus the Divine Name for forty (Shulchan Arukh, Orach Chayim 11:14). The Gra's commentary traces this structure to the Rosh and Mordechai, who held that the knots should be made from the winding strand itself rather than from the white and techelet threads together as Rabbeinu Tam and the Ri held, and he notes a dispute among the Tosafists over whether the progression of seven-nine-eleven-thirteen windings refers to windings or to chulyos (Beur HaGra on Shulchan Arukh, Orach Chayim 11:14). The Beit Yosef lays out the underlying positions of Rashi, Tosafot, the Rosh and the Mordechai on how many white and techelet strands are taken and how the Rambam's own formulation differs from theirs (Beit Yosef, Orach Chayim 11:1). The Tur likewise records the practice of tying two knots, winding the long strand around the seven, and notes that the Rambam's custom was to wind the chulyos as in the days of techelet while the Rosh did not insist on precision in this (Tur, Orach Chayim 11).
Tosafot on Menachot trace the five-knot custom to Rabbeinu Tam, who tied the knots two near the garment and three near the strands themselves so as to end with white, giving a reason rooted in the principle of elevating rather than lowering in matters of holiness, while noting that no explicit source in the Talmud fully supports this reckoning (Tosafot on Menachot 39a:10). The Gemara's own discussion of the minimum seven chulyos corresponding to the seven heavens, and the requirement of a knot between each chulyah to distinguish them, underlies these later shitos (Menachot 38a-43b), as does Tosafot's earlier comment on how the techelet and white strands may be assembled without one being mevatel the other (Tosafot on Menachot 38a:4). The Sefer HaChinukh, following the Rambam's structure, describes five double knots with three windings between each and four before the last, summing to thirteen, citing the Gemara's requirement of a thumb's-width gap from the edge (Sefer HaChinukh 386:5).
Shulchan Arukh HaRav records that when techelet was available the Sages required no fewer than seven chulyos corresponding to the seven heavens with a knot ending each chulyah, but that now, lacking techelet, there is no need to be precise about the number of chulyos or knots between them, though the universal custom from ancient times has been to make five knots, tied to the pasuk about remembering all the mitzvos (Shulchan Arukh HaRav, Orach Chayim 11:1-30). The Mishnah Berurah similarly states that the number of windings, chulyos, and knots is not strictly required by the letter of the law but represents the optimal way to perform the mitzvah, the five knots hinting to the five books of the Torah and their doubling to the ten sefirot, directing the reader to the Beit Yosef for the reasoning behind the sets of windings (Mishnah Berurah 11:61-70). The Magen Avraham adds that technically a single chulyah and knot suffices mi'doraisa, that there is no fixed measure for the windings themselves, and that the Rosh held the chulyos should be kept even in spacing for the sake of beauty (Magen Avraham 11:19-21).
Revavos Ephraim addresses a question about tying tzitzis in the manner cited by the Kaf HaChaim in the name of the Sha'ar HaKavvanot, attributed to the Zohar in Parshas Pinchas, which calls for forming the gedil into successive chulyos (Revavos Ephraim 8:474).
Background sources round out the picture of the underlying structure these shitos are built upon: the pasuk commanding the petil techelet on the fringe (Bamidbar 15:38-41), the machlokes of Beit Shammai and Beit Hillel over the number of strands and the length left hanging (Menachot 41b:12-14), the Sifrei's ruling that the halacha follows Beit Shammai on the minimum number of threads (Sifrei Bamidbar 115:1), and the Sefer HaMitzvot's framing of tzitzis as a single unified mitzvah of techelet and white rather than two (Sefer HaMitzvot, Positive Commandments 14). The Levush discusses the minimum Torah requirement of even a single chulyah and knot before the separate ma'aseh of winding and knotting is added for the mitzvah min hamuvchar (Levush, Orach Chayim 12:3), the Shulchan Arukh and Rema address the separate question of linen versus wool strands in the absence of techelet (Shulchan Arukh, Orach Chayim 9:2), the Kaf HaChayim discusses the timing of the brachah relative to wrapping (Kaf HaChayim on Shulchan Arukh, Orach Chayim 8:3), the Igros Kodesh discusses machine-spun tzitzis threads made lishmah (Igros Kodesh letter 407), the Radbaz discusses the chiyuv of a doubled garment (Teshuvot HaRadbaz Volume 6 2269:2), the Biur Halacha discusses the laws of a tear in the corner before the fringes are affixed (Biur Halacha 15:5:1), the Piskei HaSiddur discusses the required distance of the hole from the edge of the corner (Piskei HaSiddur, Tzitzit 9-10), and the Gemara passages in Menachot and Sukkah discuss related foundational requirements such as spinning lishmah (Menachot 38a-43b, Sukkah 9a:9-11).