I just did a quick survey of online articles about “how to put on a tallit,” and it seems everyone left out a key step.
Let’s take out the Shulchan Aruch, turning to O.H., Siman 8, which explains how to don a tallit. Paragraph 7 tells us to untangle the strings. Paragraph 9 tells us to make sure the strings are intact. And sandwiched in the middle is a halacha telling us as follows: “One should have in mind, when wrapping himself in a tallit, that the Blessed One commanded us to wrap ourselves in it, in order to remember all of His mitzvahs and fulfill them.”
This is no passing matter! (I keep picturing a slick Aish.com how-to video including that step by showing a bubble pop up over the head of the person donning the tallit, revealing his thoughts.)
The Mishnah Berurah adds that this is in addition to having the intention of fulfilling the mitzvah of tzitzits itself.
The Bach adds an interesting note. He says that although generally one can fulfill a mitzvah regardless of what he is thinking, three mitzvahs are different: tzitzit, tefillin and sukkah. Tzitzit, because the verse says, “in order that you remember,” tefillin, because another verse says, “in order that Hashem’s Torah be in your mouth,” and sukkah, because the verse says, “in order that your generations may know.”
The Pri Meggadim and the Mishnah Berurah add that the Bach’s requirement is in order to fulfill the mitzvah properly, but nevertheless if one did not have the right intention in mind while putting on his tallit, he still carries out the mitzvah.