Important laws to remember for Mivtzaim:
*Below is a very brief sketch of the background and some of the important reminders necessary during Mivtza Tefillin. For further Halachic information, one is to refer to the previous chapters, each according to its subject.
The times: For purposes of Mivtzaim, one may put on Tefillin starting from Mi Sheyakir until nightfall. However, once it is after sunset a blessing is not to be recited, although those who are lenient have upon home to rely.
Jewish identity: If a person is unsure whether his mother is Jewish, then one is not to put Tefillin on him, until his Jewishness is verified for certain. If one says his mother is Jewish, he may be believed regarding the Mitzvah of Tefillin. In any case of doubt of a person’s Jewishness one is to speak to a Rav who is expert in these matters to determine the severity of the doubt and whether one may put Tefillin on the person.
Is a Shoteh/Insane to put on Tefillin? A Cheresh and Shoteh are not obligated to wear Tefillin. However, they may choose to do so as long as they are able to maintain a clean body.
May one put Tefillin on a person who is in a coma or is unconscious due to brain damage? A person who is unconscious or in a coma is not to have Tefillin placed on him. However, if the patient is completely clean some write that the relatives may do so if they feel the patient subconsciously feels the Tefillin and is strengthened by it.
Putting Tefillin on ill patients in a hospital: If the patient cannot control his bowels and hence contains diapers and the like, then he may not have Tefillin placed on him while he is dirty. If he is in a coma there is no need to put Tefillin on him. However, the relatives may do so if they choose.
May people who are defined as Reshaim put on Tefillin? Yes. Not only are they allowed to wear Tefillin, but Hashem desires that Reshaim put on Tefillin even more than Tzaddikim, and it is specifically for Reshaim that the Mitzvah was given, in order to direct them to the proper path, and they need this Mitzvah even more than the Tzaddikim. [Accordingly, it is certainly permitted and a great Mitzvah and obligation for non-religious Jews to wear Tefillin, and be influenced to do so. This especially applies in today’s times where the majority, if not all, of the non-religious Jews are defined as Tinokes Shenishbu, and hence do not even enter the category of Reshaim which is discussed above.]
May a male who r”l became a transvestite/transgender wear Tefillin? Yes, he remains obligated to wear Tefillin even if he went through SRS, or gender reassignment surgery r”l. However, he is to only do so in private if his outward appearance will make others think that he is a woman.
May one do Mivtzaim in a public area where immodest women may walk by? Yes, although the person may not say a blessing or any Torah words in her presence, until he turns around [or if not possible, closes his eyes].
The arm: The Tefillin is to always be placed on the left arm unless one writes with only his left hand, in which case it is to be worn on the right arm. Prior to putting on the Tefillin one is to ask the individual as to with which hand he writes with.
Missing arm: If the left arm of a right-handed individual was amputated above the bicep, he is exempt from putting on the arm Tefillin. If it was amputated below the bicep, then he is to put on Tefillin on both arms without a blessing. If the right arm was amputated, that he needs to put on Tefillin on his left arm with a blessing.
Cast: If one has a cast or bandage on his bicep, then he is to wrap the Tefillin over the cast/bandage without a blessing, and cover the hand Tefillin with his clothing. [However, upon placing the head Tefillin the blessing of Al Mitzvas Tefillin is to be said.] If doing so is not possible, then he is exempt from donning the hand Tefillin. If the bandage/cast does not reach up to one’s bicep, then he is to wrap the Tefillin as usual over his bicep with a blessing and wrap the straps on top of the bandage or cast.
The Kavanah: The person wearing the Tefillin must intend to perform it in order to fulfill the command of Hashem. One is to explain this to the individual if there is any doubt as to whether he is aware of it. If he was unaware and only after he removed the Tefillin understood that this is a command of G-d in the Torah then he is to re-wear it.
The blessing: It is permitted to teach an adult a blessing during his time of obligation and have him repeat word after word, including Hashem’s name, from the person educating him. It is forbidden for one to recite the entire blessing to the person and then have him recite the entire blessing after him, and rather it must be recited word after word. In all cases that a Siddur is available, and the person knows to read from the Siddur, one must provide him the Siddur rather than read word after word.
What to say while wearing the Tefillin: During Mivtzaim, the people wearing Tefillin are to read all three Parshiyos of Shema. [It is proper for him to also recite Birchas Hatorah prior to saying Shema, if he has yet to say it that day.] At the very least they must read the first two Parshiyos of Shema. If there is absolutely no time available, the person fulfills his obligation even if he does not say anything at all while wearing it.
Removing watch: From the letter of the law, it is permitted to have a Chatzitza under the areas of the straps that are on the arm, and hence it is permitted to wrap the straps over a watch that one is wearing. Accordingly, there is no requirement by Mivtzaim to make sure that the person removes his watch.
Altering the knot of the Tefillin Shel Rosh so it fit his size? The straps of the head Tefillin must be tightly fastened onto one’s skull and may not be loose. If necessary, one is to change the size of the knot in order so it fit his head. When redoing the knot, it is proper for it to be fastened strong and not remain loose. Prior to shortening or widening the straps through undoing the knot of the Daled, one is to recite Lesheim Kedushas Tefillin.
Putting on only Shel Rosh or Shel Yad: On Mivtzaim, one may put on just the Shel Rosh or just the Shel Yad if he will not have time to wear both Tefillin, or does not want to do so
How is one who is left-handed to wear Tefillin of one who is right-handed [or vice versa]: One is to place the Tefillin on his right arm backwards, having its backside [i.e. Ma’abarta] be positioned in front facing towards the elbow, in order so the knot be facing inwards. When wearing the Tefillin in such a way one must be careful that the Tefillin be properly wrapped to the bicep, without it folding over. However, one should not follow the option of placing the Tefillin on as normal with the Ma’abarta facing the back, thus causing the knot to be on the outer side.
No shirt: One is not to place on Tefillin if his heart is revealed, which means that the top half of his body is not covered [i.e. no shirt; bare-chested]. By Mivtzaim, one should offer him either his own shirt or jacket prior to putting it on him.
 See Chapter 1 Halacha 5
 See Chapter 1 Halacha 6
 See Chapter 1 Halacha 6 in Q&A
 See Chapter 1 Halacha 7 in Q&A
 See Chapter 1 Halacha 6-7
 See Chapter 1 Halacha 7 in Q&A
 See Chapter 1 Halacha 6 in Q&A
 See Chapter 5 Halacha 16 in Q&A
 See Chapter 2 Halacha 6
 See Chapter 2 Halacha 6C
 See Chapter 2 Halacha 3
 See Admur 484:4 regarding running a Seder for the ignoramuses “If they do not know to say Birchas Hamazon, he is to read it with them word after word and it is not considered a blessing in vain being that they are answering after him word after word and is similar to one who is reading to a child and is teaching him Birchas Hamazon after he eats.” [Admur ibid; Michaber 484:1; Tur in name of Rosh; Maharitz Geios 2:105; Mishneh Sukkah 38 as explained in Biur Hagr”a ibid; Taz 484:3; P”M 484 M”Z 3] This does not contradict the ruling in 215:2 that one may only educate a Katan in blessings and not a Gadol, being that there it refers to “not during the time of their obligation” while here it refers to the time of their obligation. So is also implied from Rebbe in Igros Kodesh ibid who writes “since one can educate the Gadol during the time of his obligation therefore one may not do so at times that he is exempt.” However perhaps one can differentiate and say that from 484:4 we learn that only in a case that one has no ability to be Yotzei the person by telling him the blessing [i.e. Birchas Hanehnin] is it permitted to have him repeat word after word, although in a case that he can be Motzi him [i.e. Birchas Hamiztvos] then he may not repeat word after word, and must rather be Yoztei him. So is also implied from Admur 484:3 from the fact that he says that the person leading the Seder is to recite the blessing of Matzah and Maror on their behalf and does not mention repeating word after word, and only in 44:4 regarding Birchas Hanehnin does he mention it. Nonetheless, it is implied from the Rebbe ibid that it is permitted to teach him the blessings even by Birchas Hanehnin. See Hearos Ubiurim Tzemach Tzedek 3:
 P”M 484 M”Z 3; See also Shaar Hatziyon 484:7 in explanation of Michaber 167:19, however it is possible to explain in the Michaber that the person is not repeating the blessing after the person saying it but rather listening and being Yotzei
 See Hearos Ubiurim ibid in name of Rav SZ”A
 See Chapter 1 Halacha 4
 See Chapter 2 Halacha 13
 See Chapter 1 Halacha 8; Chapter 2 Halacha 10E
 See Chapter 2 Halacha 5
 See Chapter 2 Halacha 6B