It is forbidden to ignite a fire on Yom Tov. Included in that restriction would be striking a match on Yom Tov. It would be forbidden whether you want to light your ovens with it, or light a cigarette, etc. One who needs to light the oven or cigarette can do it from an existing flame. Even the lighting Nerot (candles) on the second night of Yom Tov can only come from an existing flame.
Now, there’s another restriction. It’s forbidden also to extinguish. So one has to be very careful to remind his wife that after she finishes cooking on Yom Tov, that she is not allowed to close the ovens and shut the pilots.
Regarding extinguishing a flame or match that was lit by an existing flame, one is not allowed to simply throw such a match down in a way where it will obviously extinguish. Also, one is not allowed to blow out the flame on Yom Tov. In the case of a match, the Halacha says you should just put it down and let it go out by itself. Of course you shouldn’t put it down in a dangerous place where it can burn anything. You should put it down in a place where it will not burn anything and it will go out by itself.
For that matter, on Yom Tov, the ladies can not close ovens after it’s turned on. But it is permissible to program a timer in advance, to shut off an oven.
Or for example, a lady is cooking on a gas oven or stove, and the food is on it and it’s going to burn, so it would be permissible to lower the flame a little, because that’s already extinguishing for the purpose of preparing foods. Or let’s say, the flame is there and they want to make it higher in order to enhance the foods, so of course it would be permissible to make it higher. But to begin the fire from nothing, or to close it totally, that would be forbidden.
Another example we discuss today is about a person who wants to save on his gas bill, so he wants to turn off the gas oven or stove on Yom Tov after finishing up the cooking. Such a reason is not for Tzorech Ochel (for the purpose of preparing a meal), and therefore it is forbidden. Even though it might ‘eat’ at him that he has to spend money, but nevertheless, that was not what the Chachamim had in mind.
So again, there is a restriction of igniting on Yom Tov, and there is a restriction of extinguishing. They are both forbidden on Yom Tov.
