139:12 On the first night, the one lighting the candles recites three brachos: that G-d has commanded us to kindle the Chanukah lights, that He performed miracles for our ancestors, and that He has kept us alive and sustained us to reach this occasion. This third bracha – shehechiyanu – is not recited on subsequent nights. (If one forgot to recite shehechiyanu on the first night, he recites it on some subsequent night, when he remembers – OC 676:1. If he remembers after lighting, he can no longer say it that night – Mishnah Brurah 676:2.)
After reciting the brachos, one lights one candle; while lighting the rest, he recites “HaNeiros Halalu,” that we light the candles because of the miracles, etc. (Some say HaNeiros Halalu after lighting all the candles; this is also an acceptable practice – MB 676:8.) A convert recites that G-d performed miracles “for Israel,” though if he says “for our fathers,” it is valid. (Mishnah Brurah 675:14 only says that a convert may recite the same text as everyone else.) An onen* should not light if another person (such as his wife – MB 670:12) is available to do so. Rather, the other person lights with the brachos and the onen responds Amen. If there is no one else available, the onen should light but not recite the brachos.
*One who has lost a close relative that has not yet been buried. An onen is not supposed to perform mitzvos.
139:13 Lighting the candles fulfills the mitzvah, that is to say that the act of lighting is itself the mitzvah. Therefore, when lighting, the candles must be in place and have enough oil. This is to the exclusion of lighting a menorah below three handbreadths or above twenty cubits, then moving the burning candles to an acceptable location; doing so would not be valid. (After the fact, lighting under three handbreadths is valid – MB 671:26.) Similarly, if there was not enough oil at the time of lighting and he added more oil to it after, it doesn’t help. (Rather, he must extinguish the lamp, add oil, then re-light without a bracha – MB 675:8.) Also, if one put the candles in a very windy place where they are likely to be blown out, he has not fulfilled out the mitzvah and must light again without reciting the brachos. On the other hand, if he put the menorah in an appropriate place and the candles happened to go out, the mitzvah has been fulfilled. In any case, the practice in such event is to relight them. The practice is not to light one candle from another; rather, we light from the “shamash” or from some other candle.