אין צדין דגים מן הביברים: הגה אפי' במקום שאינם מחוסרים צידה לפי שהביבר רחב הרבה והדגים נשמטים אילך ואילך: (המגיד פ"ב)

One may not trap fish from fish pools. Rema: Even in a place where they do not require trapping, since the pool is very wide and the fish slip away in all directions. (HaMagid ch. 2)

Fish, fowl, and animals that are muktzeh — one may not water them on Yom Tov and may not place food before them, lest one come to take from them. And anything that is forbidden to eat or use because it is muktzeh is forbidden to handle.

Even doubtful trapping is forbidden — for example, traps for animals, fish, and fowl that were spread out before Yom Tov, and the next day one finds things in them — they are forbidden unless it is known that they were trapped while it was still day. If the traps are found damaged from before Yom Tov, it is evident that they were trapped before Yom Tov.

A doubtful case of muktzeh is permitted on the second day of Yom Tov, since it is a double doubt.

If one blocked a water channel at its entrance and exit before Yom Tov, one may take fish from it on Yom Tov, since they are considered already trapped (given that the channel is narrow and they cannot slip away). (HaMagid ch. 8)

Geese, chickens, and doves that are in the house or courtyard and are designated for eating — one may trap them and they do not require prior designation.

All other animals and fowl that require trapping — meaning one would have to say "bring a trap and we will catch it" — it is forbidden to trap them or to place food before them. Whatever does not require trapping, one may trap and place food before them.

A deer or gazelle that nested in an orchard and gave birth to fawns there, and they are still small and do not require trapping — they are permitted without prior designation, but only in an orchard adjacent to the city within seventy cubits, since one's attention is upon them. The mother, however, cannot be helped even by designation, since she requires trapping.

Doves of a dovecote, doves of an upper story, and birds that nested in clay vessels built into walls for birds to nest in — it is forbidden to trap them, and therefore designation does not help for them. This applies to adult birds, but small ones that cannot yet fly may be trapped, though they do require designation.

How is designation done? One says "this one and that one I will take tomorrow" — one need not shake them. But saying "from here I will take tomorrow" is not sufficient.

If one designated the entire dovecote but only needs a pair, it is not effective. Rema: But if it is possible he will need the entire dovecote, he may designate the whole dovecote and take what he needs the next day. (Rabbeinu Yerucham and Hagahot Asheiri, ch. 1 of Beitzah)

If one designated two and found three, or designated black ones and white ones in nests separated by a partition and found the black ones in place of the white ones and the white ones in place of the black ones — they are forbidden unless he recognizes them.

If one designated three and found two, they are permitted. (And even if they were tied together, one separates them from each other.) (Beit Yosef)

If one designated birds inside the nest and found them in front of the nest, they are forbidden. If there is no other nest nearby, they are permitted. This applies when they are hopping, but if they can fly they are forbidden. And even if there is another nest within fifty cubits, if it is around a corner such that one cannot see it from this nest — since they are only hopping and not flying, wherever it hops and does not return, it is evident it belongs to that nest and has not hopped away from it. (If one designated birds inside the nest and found them at the entrance of the nest, they are permitted.) (Or Zarua)

If a non-Jew brought a Jew a gift on Yom Tov of young doves from dovecotes he owns in the city — since they do not require trapping, they are permitted.

One who slaughters an animal on Yom Tov — it is better that he not inspect it until after he skins it, because if it is found to be a tereifah he will not be permitted to skin it.

If it is found to be a tereifah, it is forbidden to handle it, but one may sell it to a non-Jew in the same manner as selling to a Jew was permitted — without weighing it and without mentioning a specific sum of money. If he does not trust him, he may take a pledge from him.