Or is it just oral tradition passed down?
The Torah just says to put on tefilin, doesn't say what to do when putting them on.
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Sign up to join this communityOr is it just oral tradition passed down?
The Torah just says to put on tefilin, doesn't say what to do when putting them on.
Like you mentioned, although the Written Torah does discuss putting on tefillin, it does not instruct how to put them on. Thus the answer to your first question, if the Torah discusses how to put on tefillin, is no.
However, the Oral Torah always has much more to say than the Written one. In Shulchan Aruch, Orach Chayim, simanim 25 - 45, discusses the halachos of tefillin. It discusses how to put them on, what to think about when putting them on/wearing them, etc. Here is a link to the Shulchan Aruch online, wear you can read a little about it. (I don't think the whole thing is translated though, so you might encounter some untranslated parts every once in a while.)
Interestingly, though, the Shulchan Aruch does not discuss the exact way to wrap the strap of the tefillin shel yad around the hand. This is minhag, passed down from one's father. So this is the reason why different regions or families will have different minhagim concerning the hand.