The Mitzvah of the Menorah cannot be fulfilled without placing the Menorah in a proper location, just as it cannot be fulfilled without being lit. It has also been established that one who holds the Menorah in his hand the entire time, even in a proper location for the Menorah, has not fulfilled the obligation (Shabbos, 22.2). It has also been established that the Menorah must be lit after being placed in a proper location, which, according to the Talmud, was at the entrance way outside. If it is lit inside and then carried to its place one has not fulfilled the requirements (Shabbos, 22.2).
From these laws above it would appear that placing the Menorah is part of the Mitzvah. Following this logic, one whose lighting of the Menorah is deemed invalid, for example a deaf person, a mentally deficient person or a minor would also be invalid for placing the Menorah in a proper location. Though this appears so it is in fact not the case, and the Talmud clearly delineates that the Mitzvah is the lighting, and not the placing. Therefore, if a deaf person, a mentally deficient person or a minor were to place the Menorah and another were to light it that would be acceptable. This distinction has numerous other resulting outcomes, as will be explained.
(Note that if it did happen that one held the Menorah in his hand, but for only a brief period of time, he has nevertheless fulfilled his obligation.)
If you should ask 'Why indeed does one not fulfill his obligation just because he is holding the Menorah in his hand?', the reason is that while being held the fact that it was lit for Chanukka is unrecognizable. One who sees this will merely say 'He is using that for his own needs, and not for any Mitzvah' (Shabbos, 22.2), resulting in no publicity for the Miracle. For the same reason it is not proper to light inside the house and then carry it outside, for those seeing will say 'This is for his own use.'
Furthermore, since the lighting is the Mitzvah one must light the Menorah while it is placed in the proper location (Shabbos, 22.2). It should noted that this only applied in earlier times, when they had a specific location for Menorah lighting (by the entrance way, outside). Today this does not apply since we light in all areas (Bach and Magen Avraham in comment 3).
Since the Mitzvah is to light, and not to place, there is also no requirement that the Menorah be placed consciously for the purpose of the Mitzvah. Therefore, if one found the Menorah already in the proper location he may light it without having to raise and lower it for with intent for the Mitzvah. This is not true in regard to lighting, where one cannot use a previously lit Menorah, and he must first extinguish it and then relight it again with intent for the Mitzvah. In fact, if the candles were originally lit on behalf of the Mitzvah as last twenty four hours until the next day one cannot use them, but must first extinguish and the relight them anew. This is the meaning of the words of our Sages of blessed memory, that a 'glass lamp that was lit throughout the day' - that is, lit for Chanukka from Friday afternoon - 'after Shabbos departs it must be extinguished and then lit again with intent for the Mitzvah.'
Know further that even though we have said that today there is no set location for lighting, nevertheless one may not light the Menorah in one location with intent to afterwards place it in another. In addition, the Menorah must be placed in its intended location with enough oil [or long enough candles] to last the proper amount of time, which is a half hour.
However, were one to place it in one location and then it became apparent that the Menorah needs to be moved and it was taken from its place one has still fulfilled his obligation in this day and age. There are those that posit that in a synagogue it is permissible to light in one place with intent to move to another (Beis Yosef), because lighting in the synagogue is simply a matter of custom, not law. Nevertheless one should preferably refrain from this practice (Magen Avraham, comment 2).
We have already written in section 671 that one is obligated to fill a Menorah with the correct amount of oil before he lights. If one only fills with a bit oil and pronounces the blessings and lights he has not fulfilled his obligation, for there needs to be enough oil at the outset to last the required amount of time, since the lighting is the actual performance of the Mitzvah, and this should be obvious.
(The fact that the Beis Yosef attributed this law to 'others who say' is simply the style of the Shulchan Aruch when only one authority mentions the law. It should also clear that if oil is added after the blessing but before the lighting the obligation is considered fulfilled.)
Women can light the Chanukka Menorah and fulfill a man's obligation on his behalf as well, for a woman is just as obligated in the Mitzvah as a man, as they were also beneficiaries of the miracle. Moreover, through their agency a specific miracle occurred, as I have written in chapter 670.
One who is deaf, mentally deficient or a monor does not light, even if the placement is handled by an adult [or one otherwise in possession of his faculties], since we have previously explained that the core obligation is the lighting, and not the placement. There is a dissenting opinion that permits a minor who has reached the age when he can be educated to light on behalf of adults (ran, in the name of the Itur). This opinion is actually following the ruling of the Talmud Yirushalmi in Megillah, where it states that there had been a custom to allow a minor to read the Megilla [on Purim, on behalf of others]. Nevertheless, all the early authorities do not support this, and we have no custom of allowing a minor to read the Megillah. Though this be so, if every member of a household lights for himself a minor who has reached educable age may also light for himself.
One who has already lit may recite the blessings for another, or for a woman, if they are unable to light and recite the blessings themselves. If they choose this approach, they must stand nearby and the one who recites must have intent to be pronouncing the blessings on their behalf, as is the requirement for reciting any Mitzvah-related blessing for another. Regarding this class of blessings the general rule is that one who has already fulfilled his personal obligation can still fulfill the obligation that another has to recite a blessing.
One who is blind - some rule that he is obligated to light the Menorah, even though he cannot see it, since one is not required to derive any benefit from the light. Nevertheless, if he can join another's lighting through contributing a nominal amount to purchase 'a share' of the Mizvah he should do so. [If he does not join with another and] he has a wife, his wife should recite the blessings for him. If he has no wife he should make the blessings himself and another should assist him in lighting if he cannot do so himself [safely] (Magen Avraham, comment 4). Others dispute this ruling and state that a blind person does not recite the blessings. This is the proper approach as the primary purpose of the Mitzvah is to be reminded of the miracle by seeing the candles, and this one cannot see them. Therefore, the proper practice if at all possible is that that a blind person not recite the blessings.