After a funeral, one of the first things an immediate relative of the deceased does upon returning home is to light a candle in the deceased's memory.
On the annual Yarzeit (anniversary of the deceased’s passing), immediate relatives will again light a candle. If the Yarzeit is a Shabbat, the candle is lit before kindling Shabbat candles.
Immediate relatives for these purposes include a spouse, child, sibling and parent.
A candle is also lit on Erev (eve of) Yom Kippur, in memory of a deceased relative. This candle is kindled before the Yom Kippur candles.
Typically, a “Yarzeit candle”, commonly found in Jewish food and book shops, is used for all of the above lightings.
Although there is no prescribed prayer to be said before lighting the candle. it is nevertheless appropriate to have in mind that God should grant continued compassion to the souls in whose honour the candle is being lit.