Beitzah, Chapter 4, Mishnah 5. Most of our Mishnah deals with additional cases of fashioning vessels on Yom Tov, and many of them relate to cooking or to fire.
"Ein shovrin es hacheres ve'ein choschin es haniyar litzlos bo maliach":
One may not break a piece of earthenware or cut a piece of paper in order to roast a salted fish on it. The usual method of roasting was to place the fish on a shard of earthenware or on a piece of paper, which prevented it from being scorched by the heat of the metal on which it was placed, such as a pan. Breaking or cutting for this purpose is forbidden, because through this act a person produces a vessel, a functional utensil, on Yom Tov.
"Ve'ein gorfin tanur ukirayim":
The oven was used for baking, and the kirayim was a type of stove on which food was cooked. And this is the distinction between raking out and pressing down:
Raking out - forbidden: One may not take the coals that are inside them and rake them out, since this too involves fixing a vessel and fashioning it. Until now nothing could be placed on it because of the uneven surface, and through the raking the surface becomes level and usable.
Pressing down - permitted ("aval mechabshin"): One may press the ashes inside it downward so that it will be level and even, since here there is no fixing of the vessel, only preparing its condition for use on a temporary basis alone.
In practice, the halachah is that if it is impossible to cook on it without raking out, then even raking out is permitted.
"Ve'ein makifin shtei chaviyos lishpos aleihen es hakedeirah":
One may not stand two barrels alongside one another in order to place the pot on them and kindle a fire between them, since by doing so a form of building is created, at the very least a temporary structure. In other words, a person thereby makes a kind of oven or stove.
"Ve'ein somchin es hakedeirah bivkas, vechein badeles":
With a pot: One may not prop up the pot with a piece of split wood.
With a door: Likewise, one may not use a small piece of wood to prop up a door.
The reason for this is that wood is generally muktzeh, unless it was designated for a particular purpose. A piece of split wood normally stands ready for kindling on Yom Tov, and therefore it is set aside for that purpose, and it may not be used for any other purpose, such as propping up an object.
"Ve'ein manhigin es habeheimah bemakel beYom Tov":
This is a halachah unrelated to the preceding ones: it is forbidden to drive an animal with a stick on Yom Tov, because it looks as though one is leading it to the marketplace to sell it, and selling an animal on Yom Tov is forbidden. Rabbi Shimon permits it, since in his view it does not appear that way, and therefore it is permitted.
In summary: In this Mishnah we learned the prohibitions of fashioning and fixing vessels on Yom Tov: breaking earthenware and cutting paper to roast salted fish, raking out an oven and a stove (as opposed to pressing down the ashes, which is permitted), setting up two barrels to rest a pot on them because of the building involved, and propping up a pot or a door with a piece of split wood because of muktzeh. Finally we learned the prohibition of driving an animal with a stick because it appears as though one is selling it, and the opinion of Rabbi Shimon who permits it.