The mitzva is fulfilled by the act of lighting the candles, not by having them lit. This is evident from the formulation of the berakha: “Who has sanctified us with His mitzvot and commanded us to light Ĥanuka candles.” Therefore, if one lights candles that can burn for half an hour and someone knocks them down by accident, causing them to go out before half an hour has passed, he does not need to rekindle them, because he fulfilled the mitzva when he lit the candles initially. Even if one lights inferior candles, such that there is some concern that they might go out, he has discharged his obligation, assuming that these candles usually last for half an hour. Nonetheless, the Aĥaronim rule that it is proper to be stringent and rekindle the candles, so that they may be lit for the half-hour period that the Sages prescribed (sa 673:2, mb ad loc. 27).
However, if one lights the candles in a place where they cannot burn for half an hour, like in a windy area, and the wind actually blows them out before they manage to burn for half an hour, he has not fulfilled his obligation, because at the moment he lit them they were not fit to last the required amount of time. Most poskim maintain that in such a case one must rekindle the candles with a berakha, but in practice one should rekindle them without a berakha, because the matter is uncertain, and the rule is that we are lenient in cases of uncertainty concerning berakhot.
As previously stated, the mitzva is fulfilled by lighting the candles, not by placing them in their proper place. Therefore, if a candle happened to have been lit while it was still daytime, and it is situated in a valid location for Ĥanuka candles, one has not fulfilled his obligation, since it was not lit for the sake of the mitzva. Even if one picks up the lit candle and then puts it back down with the intention to perform the mitzva, he has not fulfilled his obligation. Rather, he must extinguish it and rekindle it for the sake of the mitzva, and there is no need to pick it up and put it back down (Shabbat 23a, sa 675:1).
One must light the candles where they will be placed. Even if the head of the household is ill and cannot get out of bed, one may not bring the candles to him so that he can light by his bedside, and then transfer the candles to their proper place. Rather, the head of the household may recite the berakhot while someone else lights for him in the proper location of the candles (Ben Ish Ĥai, Year 1, Hilkhot Ĥanuka 6 [Vayeshev]). If one places the candles on the windowsill, but forgets to move them close to the window before lighting, he may push them closer after the lighting, so that the passersby can see them more clearly.
According to Maharshal and Taz (mb 673:26), if the candles accidentally go out late Friday afternoon before Shabbat, one must rekindle them, because they have not yet burned after shki’a. Most poskim, however, maintain that while one is not obligated to rekindle the candles in this situation, it is very proper to do so. After Shabbat begins, or after one accepts Shabbat upon himself, everyone agrees that one may not relight the candles.
. If one moves the candles from inside to outside, or vice versa, after the lighting, he has not fulfilled his obligation, because an onlooker might think that he lit them for his own use (sa 675:11). Regarding nowadays, this requires further investigation. After all, people today do not use candles for light; therefore this concern no longer applies. In practice, though, one should not move the candles from place to place, even inside one’s home (mb ad loc. 6). It seems, however, that one may move them slightly, when it is clear that one’s intention is to publicize the miracle more effectively. See sht 674:4, Yemei Ha-Ĥanuka 6:33, Hilkhot Ĥag Be-ĥag ch. 9 n. 26.