אסור לכבות דליקה בי"ט ואפי' אם רואה ביתו שנשרף אם אין שם סכנת נפשות ואין מכבין הבקעת אפי' כדי שלא יתעשן הבית או הקדירה או כדי לשמש מטתו: הגה ויש אומרים דוקא אם אפשר להציל הקדירה בלא כבוי אבל אם אי אפשר להציל או לבשל הקדירה בענין אחר רק שיכבה מותר לכבות [הרא"ש ומרדכי ור"ן פ"ב דביצה ורשב"א וטור] וכן נראה לי עיקר וכן בבית אם ישרף הבית לא יהיה לו מקו' לאכול שם ויפסיד סעודתו מותר לכבות אבל אם יש לו בית אחר לאכול שם אסור לכבות משום הפסד ממונו [ב"י בשם אורחת חיים] :

It is forbidden to extinguish a fire on Yom Tov, even if one sees his house burning, as long as there is no danger to life. One may not extinguish a piece of wood even to prevent the house or pot from becoming smoky, or in order to have marital relations. Rema: Some say this applies only when it is possible to save the pot without extinguishing, but if it is impossible to save or cook the pot in any other way except by extinguishing, it is permitted to extinguish. [Rosh, Mordechai, Ran ch. 2 of Beitzah, Rashba, and Tur] This seems to me the primary ruling. Similarly regarding a house — if the house will burn and he will have no place to eat there and will lose his meal, it is permitted to extinguish; but if he has another house to eat in, it is forbidden to extinguish on account of financial loss. [Beit Yosef in the name of Orchot Chayyim]

Tilting a lamp to draw the oil away from the wick is considered extinguishing and is forbidden. Similarly it is forbidden to take a wick from a burning lamp even to place it in another lamp, since the moment one removes it one extinguishes it. Rema: It is permitted to add wicks to a burning lamp so that it burns strongly and goes out quickly. [Ran, ch. Ein Tzadin]

A wax candle that one wishes to light on Yom Tov, and one is concerned it will burn down entirely — one may place around it before lighting it something that prevents it from burning, so that it will go out when the flame reaches that point. Rema: Some permit cutting a wax candle with fire — meaning one lights it also from below in order to shorten it — and this is the custom. But cutting it with a knife is forbidden. [Hagahot Maimoniyot ch. 6, Hagahot Asheiri, Mordechai, and Tosafot ch. 1 of Beitzah] It is permitted to place a lamp in a spot where the wind blows in order for it to go out, but it is forbidden to place it there if the wind is already blowing. [Maharil]

A lamp that went out and one wishes to relight it that same day — one may trim the top of the wick so that it will be easy to light. Rema: Leftover oil and wicks are permitted even on Yom Tov that follows Shabbat, or the two days of Rosh Hashanah. (Beit Yosef in the name of most authorities)

A lamp lit for no purpose — meaning one does not need it — it is forbidden to light. But a synagogue lamp is not considered purposeless and it is permitted to light it even on the second day of Yom Tov after Mincha, and there is no concern of preparing for a weekday, since in lighting it there is a mitzvah for that moment. To fix the wicks and the lamps on Yom Tov after Mincha — if one wishes to light them that same day it is permitted; if not, it is forbidden.

One may not place a lamp on a tree from before Yom Tov, since we are concerned one may come to make use of the tree.

One may not open a clay lamp — meaning while it is still soft like a potter's clay vessel — by pressing it with one's hand to make a hollow in it, since one would be making a vessel.

One may not cut a wick in two, unless one inserts both its ends into two lamps and lights it in the middle, and only when one needs both lamps.

One may not braid a wick nor singe it; but if it is not hard enough one may press it with one's hand to harden it, and it is permitted to soak it in oil [in which there is no burning lamp]. [Beit Yosef in the name of the Rokeach]

It is permitted to remove the charred tip from the top of a burning lamp, but one may not cut the top of the wick with a utensil.

One who lights a Yom Tov lamp must recite the blessing: Blessed are You, Lord our God, King of the universe, who has commanded us to light the Yom Tov lamp.