Beitzah, Chapter 4, Mishnah 4. This mishnah opens with a discussion of making a lamp on Yom Tov, and along with it, the subject of utensils connected to fire.
"Ein pochasin es haner":
The mishnah rules that one may not fashion a lamp on Yom Tov. Some have a different version of the text - "ein posechin es haner" - and both versions point to the same idea: that one may not fashion a lamp.
How would they make a lamp? They would take a ball of clay, press a fist into it and form a reservoir for oil inside it, and into that they would insert a wick. This explains the different wordings:
"Pochasin" - from the root meaning to diminish: pressing the hand into the ball of clay reduces it in that area.
"Posechin" - from the root meaning to open: opening the cavity formed in the clay for the lamp.
On Yom Tov this is forbidden, because through this act a person is fashioning a utensil.
"Ein osin pecham'in b'Yom Tov":
Continuing with the subject of making utensils, the mishnah rules that one may not make charcoal on Yom Tov. Why is charcoal considered a utensil? Because it was used in craftsmanship, in melting gold, and since it served the function of a utensil it was viewed as a type of utensil. Therefore one does not make charcoal on Yom Tov.
"V'ein chotchin es hapesilah lishnayim":
One may not cut a wick in two - for example, someone who has one long wick and wants to use it for two lamps - because he is taking one utensil and making two out of it.
The view of Rabbi Yehudah:
Rabbi Yehudah says that there is a permitted method: "Chotchah ba'ur lishtei neiros" - cutting the wick by means of the fire itself, so that it can serve two lamps. How so? He takes the long wick, places its two ends into two lamps that contain oil, and lights it in the middle. In this way it burns and divides into two wicks in two lamps.
This is permitted because it is not done in the direct manner of fashioning a utensil, but rather in an indirect manner, through kindling a fire alone, which is permitted on Yom Tov.
In summary: In this mishnah we learned that one may not fashion a lamp on Yom Tov (according to both wordings: "pochasin," from the root meaning to diminish, and "posechin," from the root meaning to open the cavity), that one may not make charcoal - which is also considered a utensil because of its function in melting - and that one may not cut a wick in two, since one utensil is being made into two. Rabbi Yehudah adds that it is permitted to cut the wick by means of the fire, since this is an indirect method of kindling and not the fashioning of a utensil.