If you are thinking of tying techelet tzitzit on your next tallit or tallit katan, but are not sure which tying custom to follow, you’re not alone.
With all white tzitzit, usually there’s nothing to decide: if you’re Ashkenazi, you tie Ashkenazi, if you’re Sephardic, you tie Sephardic, if you’re Chabad, you tie Chabad. But since it’s highly unlikely your parents, grandparents or great-grandparents had techelet tzitzit, you have no tradition to follow, and are left in a bit of a quandry.
The first thing you need to know is that tying techelet tzitzit according to the Ashkenazi or Sephardic custom is not the correct way to go about it. These customs were developed in the absence of techelet, but the Gemara provides many details about how to tie tzitzit and the Ashkenazi and Sephardic tying customs for all-white tzitzit do not meet many of the requirements in the Gemara.
Namely, the Gemara speaks of chulyot, saying you must have a minimum of seven and a maximum of thirteen. Normally chulyot are understood to be sets of three windings. Thus, for example, the Vilna Gaon writes that you should do thirteen chulyot as follows: after the first double knot, do 3 windings using the white shamsash string, three with the blue, three white, and three blue, i.e. four chulyot. Then make a second double knot. Repeat this sequence another three times so that you have a total of 12 chulyot. Then do one final chulyah of white and tie a final double knot.
Some of the other approaches, such as Sefer HaChinuch and Amram Gaon, are quite similar, while the Rambam and the Arizal have different approaches regarding how to create the chulyot.
If you insist on following the standard Ashkenazi or Sephardic tying custom, at least be sure that the very first and last windings are white, a basic requirement that the Gemara states unambigiously.
If you have the opportunity to delve into the topic, you’ll find the discussion starting on Menachot xxb. To see images of the primary techelet tying approaches, refer to this guide.
From a halachic standpoint, even more important than which tying custom you follow is how many strings of blue you use. We know four tzitzit strings must be tied onto each corner. Once they are tied you see what appears to be eight strings hanging down. The Torah refers to a פתיל תכלת in the singular, but does that mean one of the four strings, i.e. one complete string of blue, or one of the eight strings, which would be achieved by using one string that is half blue and half white? The Rambam holds that one of the eight strings must be blue, while the Raavad holds that two of them must be blue. (The Tosefot has another approach according to white half of the eight strings should be blue.)
The Arizal and others agree with the Rambam, while the Gra, Sefer HaChinuch and others side with the Raavad. In practical terms, some say that today, in the absence of a mesorah, Ashkenazim should follow the Raavad, while Sephardim should follow the Rambam. But not all rabbanim agree with that approach, and it is recommended that you consult your rabbi on this question.