When to light it: It is forbidden to light a candle on Yom Tov unless its light is needed for the room. Therefore, those who have a Yartzite on Yom Tov are to light the Yartzite candle before Yom Tov. Likewise, those who light a Yizkor candle, are to light it before Yom Tov. [Accordingly, in Eretz Yisrael, a 24-hour candle is to be lit before Yom Tov, while in the Diaspora a 48 hour candle is to be lit before Yom Tov.]
Lighting in Shul if one did not light the candle before Yom Tov: One who did not light the Yartzite/Yizkor candle before Yom Tov may light it on Yom Tov inside an active Shul, [in the room where the prayer takes place]. One is not to light the candle in one’s home on Yom Tov, unless it is lit in an area that is dark and one intends to also use the light in order to see in the room.
Lighting at home if one cannot light in Shul: In a case that one did not light the candle before Yom Tov and one is unable to light the candle in Shul, some Poskim rule it is permitted to light the Yartzite candle at home, even if there is enough light in the room without the candle. Nonetheless, initially in such a case, one is to light it near one’s dining room table prior to the night meal, thus giving it a use for one’s meal. However, if this too is not possible, then one may light it in any area that he desires. Other Poskim however argue and rule one may never light a candle at home if one does not need its light. [Practically, one may be lenient in a time of need regarding a Yartzite candle, for one who has a Yartzite of a parent on Yom Tov. However, a Yizkor candle should not be lit on Yom Tov.]
Asking a gentile to light the candle: In all cases that one did not light a Yartzite or Yizkor candle before Yom Tov, it is permitted to ask a gentile to light it for him.
Lighting a candle for other relatives: The above leniency of lighting a Yartzite/Yizkor candle on Yom Tov in one’s home only applies towards the Yartzite or Yizkor of one’s parents, and not other relatives. It is forbidden to light candles on behalf of other relatives inside one’s home, if one does not need the light. Even in Shul, one is not to light too many candles.
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 Kesav Sofer 75; Biur Halacha 514/5 “Neir”; Kaf Hachaim 514/79; Sefer Haminhagim p. 180
 See Aruch Hashulchan 514/19; Betzel Hachochma 4/29; Sefer Hachaim Hanitzchiyim 12/2
The Chabad custom: It is not the Chabad custom to light a candle for Yizkor. The Rebbe and Rebbe Rayatz did not light Yizkor candles. [Hamelech Bemisibo 1/321 [printed in Shulchan Menachem 2/250]; Heard from Rav Leibal Groner; However, in Luach Kolel Chabad it says to light it]
 See Admur 514/13-14; Biur Halacha 514/5 “Ner”; Kaf Hachaim 514/79; Piskeiy Teshuvos 514/14; Nitei Gavriel 55/2
 Admur 514/13; Michaber 514/5
 Biur Halacha ibid; Piskeiy Teshuvos ibid footnote 70; Nitei Gavriel ibid; See SSH”K 13 footnote 27
The reason: As it is forbidden to light a Ner Shel Batala on Yom Tov. [Admur 514/13; Michaber 514/5]
 Nitei Gavriel ibid
 Admur 514/14; Michaber 514/4; P”M 132 M”Z 2; Kesav Zofer 75; Biur Halacha ibid; Kaf Hachaim ibid; Piskeiy Teshuvos ibid; Nitei Gavriel ibid
The reason: One may light any candle in Shul, as it is considered a Neir Shel Mitzvah, as it gives honor to the Shul. [Admur 514/14; Michaber 514/4]
Other Opinions: Some Poskim rule one may never light a Yartzite candle on Yom Tov, even in Shul. [Daas Torah 514 in name of Imrei Eish] Some rule one may only do so through a gentile. [Kitzur SHU”A 98/1]
 P”M 132 M”Z 2; Daas Torah 514 in name of Imrei Eish 40; Kitzur SHU”A 98/1; Piskeiy Teshuvos ibid
The reason: As it does not add any light to the house even at night being that we have electricity. Thus, it may not be lit as it is considered a light that serves no purpose which is forbidden to be lit on Yom Tov. [Admur 514/13; Michaber 514/5; P”M ibid]
 Kesav Sofer 75; Biur Halacha 514/5 “Neir”; Kaf Hachaim 514/79
 Kesav Sofer ibid; Biur Halacha ibid; Kaf Hachaim ibid; Nitei Gavriel ibid
The reason: As it is permitted to light a Ner Shel Mitzvah [Admur 514/14; Michaber 514/5] and a Yartzite candle can be considered a Ner Shel Mitzvah, being that it is lit for the honor of one’s parents. [Kesav Sofer ibid; Biur Halacha ibid; Kaf hachaim ibid]
 P”M 132 M”Z 2; Daas Torah ibid; Kitzur SHU”A ibid
 The reason: As the custom of lighting a Yizkor candle is not very clear, and many even initially are not accustomed to do so. Nevertheless, one who is in great anguish that a candle is not lit and is doing so in honor of a parent, seemingly may be lenient if there is no other alternative of lighting it.
 Kitzur SHU”A ibid
 See Nitei Gavriel 56/5
The reason: As there is no Mitzvah of honoring these other relatives, and hence the candle is not coinsidreed a Ner Shel Mitzvah, but rather a Ner Shel Batala.
 Aruch Hashulchan 514/19; Nitei Gavriel 56/6