In order to remember etc. - An example of this is like a man that wants to warn/remind his friend about something, so he ties a knot around him so that he should remember (Tur).

Over his garments - See previously in Siman 8 in Mishna Berurah what was written there.

At the time of prayer (ie. Shemona Esrei) - And Kriyat Shema. And see [what's written] in the Zohar - Parshat שלח לך, that one who reads Kriyat Shema without Tzitzit testifies a false testimony on themselves. For he reads the Parsha of ציצית, but he does not fulfill [what's written in] the verse. The Chayei Adam writes "It is not good what many people do... that they pray while on their way without wearing a טלית גדול. And in most cases, the טלית קטן [that they are wearing] was not made properly with all the [Halachic] details that would make it fitting to make the blessing on. And also, they sleep in it at night...". And see [what was written] previously in Siman 8, Se'if 16 in Mishnah Berurah.

With your left hand - It is written in the writings of the Arizal that [one should] hold them (the Tzitzit strings) between the ring and pinky fingers. And when you get to the Parsha of ציצית, take them also in your right hand and gaze at them. And they should remain in your hands until you reach [the words] "נאמנים ונחמדים לעד"... at which point you kiss the Tzitzit and release them from your hands.

On your heart - For the heart is on the left [side]. And this מצוה saves a person from sin as it is written "And you shall not stray [after you heart] etc."... "in order that you shall remember etc."... "and you shall be holy". And [from the fact that] all the other מצות don't have this protective power to save a person from the evil inclination, [that's what makes] ציצית superior. And as is demonstrated in the story [mentioned in] מנחות (daf 44a) [that starts with the words] "מעשה באדם אחד" etc.

While you say the blessing - As it says "And you shall see it and remember". Seeing leads to remembering and remembering leads to doing.

Over your eyes - It's found in the name of the earlier commentators that all who pass the ציצית over their eyes when they read the parsha of ציצית is guaranteed that they won't come to be blind. A blind person should hold the ציצית in his hands while saying Kriyat Shema even though it says "and you shall see them (ie. the ציצית)", since there is the ability to see among other people. But to pass them over his eyes, he should not do, for it appears as if he is laughing and mocking [the מצוה].

To the Havayot - Meaning the Sephirot which are connected and united one with the other.

One who is careful with the מצוה of ציצית - It is a מצוה to make a fine טלית garment and fine ציצית [strings]. And the same thing applies to all the מצות... one must do them with an adornment as much as possible... as it is written "This is my God and I will glorify Him" [which the Sages interpreted anveihu (glorify) homiletically as linguistically related to noi (beauty), and interpreted the verse as] "Beautify yourself before Him in mitzvot". But it is forbidden to embroider verses from the Torah onto the טלית. Nevertheless, if it was already embroidered, it is permissible to bless on it. And even on a tablecloth, we do not teach that it is permissible a priori to embroider verses from the Torah on it.