One may slaughter an animal or bird in order to eat it on Yom Tov. He may do so even if he wants to eat only a small amount of meat, as it is impossible to attain a small piece without slaughtering a whole animal.
However, it is forbidden to trap wild animals – whether beasts, birds, or fish. The Sages even forbade feeding them, out of concern that this would lead people to trap them (Beitza 23b; SA 497:2). If animals were trapped before Yom Tov and confined to a small area where it is possible to capture them with one motion and without the help of a net, they are considered already trapped, and one may take one of these animals for a Yom Tov meal (Beitza 24a; SA 497:7; Peninei Halakha: Shabbat 20:6).
Before slaughtering the animal, it must be ascertained that the slaughtering knife is sharp and smooth. If it is nicked, the slaughter is disqualified and the animal is not kosher. On weekdays, the Sages decreed that anyone wishing to slaughter must first have a scholar look at the knife and check that it is not nicked. On Yom Tov, however, a slaughtering knife may not be shown to a scholar, out of concern that if the scholar declares it unfit, the knife’s owner would sharpen it on Yom Tov, thus transgressing Torah law. Rather, the knife must be checked by a scholar before Yom Tov. Nowadays, shoḥtim receive certification attesting to their qualification for kosher slaughter, and thus we rely upon them to know how to check their own knives. Nevertheless, a shoḥet must make sure to check his knife before Yom Tov so that he will not be tempted to sharpen it on Yom Tov. In contrast, the main local rabbi may check his knife on Yom Tov, as we are not concerned that he will end up sharpening it. He may also lend it to others (Beitza 28b; SA 498:1).
Even though Mafshit (skinning) is one of the 39 prohibited melakhot (Peninei Halakha: Shabbat 18:6), on Yom Tov one may remove an animal’s skin and place it somewhere where people will walk on it, to prevent its rotting (see BHL 498:6 s.v. “kedai”). To understand why this is so, some introductory remarks are needed. During the week, after an animal is slaughtered, its hide is tanned, that is, packed in salt and other chemicals that remove its natural moisture. This prevents the hide from rotting, and allows it to be made into clothes, shoes, or rugs that last for many years. Tanning is prohibited on Yom Tov, as on Shabbat. But the Sages were concerned that people might avoid slaughtering an animal they need for Yom Tov meals in order to avoid losing the hide, which was likely to rot before the end of the festival. Therefore, the Sages permitted skinning an animal and placing the hide where people would trample it, thus preventing its decomposition. Additionally, they permitted the salting of meat (as for roasting) on top of the skins so that some of the salt falls on the hide and inhibits decomposition. After Yom Tov the hide may be properly tanned (Beitza 11a; SA 499:3).
When slaughtering a bird or an animal categorized as a ḥaya, there is a mitzva to cover its blood with dirt afterward. Since dirt is normally muktzeh, some of it must be specifically set aside for this purpose before Yom Tov. If this was not done, the bird or ḥaya may not be slaughtered (Beitza 2a; SA 498:14).
One who wishes to slaughter a sheep or goat may not yank out the wool on its neck to make room for the knife, because this violates the melakha of Gozez (shearing). Rather, he should brush away the wool with his hands. If he unintentionally pulls out a little wool, he has not transgressed (SA 498:12). After the slaughter, one who wishes to eat the skin may not shear the wool, because people will assume that he is shearing to obtain wool. Rather, he may singe the wool off the skin (SA 500:4).
Even though one may not set aside ma’aser on Yom Tov, he may give a slaughtered animal’s shank, cheek, and stomach to a Kohen, because those gifts belong to him by Torah law from the moment of slaughter (SA 506:9).