Had to link this page because it's simple, elegant and concise. Print this page off and store it as a guide when the time comes to trap small birds and other safe game aboveground on a regular basis. You might want to experiment with building a few of these just to learn the details.
Note that scraps and leftovers including sprouts and spoiled grain serves as excellent bait for these traps, allowing you to convert a disastrous situation (discovering a barrel has leaked and fermented the contents) into a potential fresh food source for the vault.
Some facts about capturing small birds and hares after a nuclear war :
1. You should go over the catch with an alpha/beta particle detector wand when you retrieve it. If you get a ton of clicks the second you get near it, this bird has gotten into something contaminated by fallout and is too polluted with radeonucleotides to consume. Try disposing of it and reset the trap. Better luck next time, many birds will not be contaminated if they have survived off the ground eating berries or safer grub. Many hares may be reproducing quite rapidly in the post-nuclear environment and the younger ones are likely to be the cleanest or even uncontaminated. Most hares that feed on roots and vegetables will be quite safe to eat.
2. Never eat any of the internal organs as this is where the dangerous stuff tends to accumulate, in the body fats and internal tissues. Clean the game and discard everything but the meat. If you can scan this and it is clean you've still got the best protein. Beware of relying on just this resource as your only protein. The exact remedy that many mountain men relied on ... eating the internal organs to get a more complete diet, cannot be practiced following a nuclear war. So it is good to plan on supplementing this meat with other food products. Many people have starved to death in early colonial times in America eating rabbits, because the most essential parts of the human diet were missing from this menu.
3. Post-Nuclear literature has predicted several different kinds of plagues following a nuclear war and at least two of these are suitable for eating. Researchers expect a plague of insects, both on the ground and in the air, followed by a plague of birds, followed by a plague of hares, a plague of rats. At certain times in Medieval England, the wilderness was sometimes overrun by rabbits so thickly populated that one could wade through them and snatch them up by the ears with almost no effort. Eating rats and insects is left to vault-dweller discretion. It might be possible to capture unlimited numbers of birds and hares each day by simply resetting traps aboveground near the shelter entrance. The strategy described should take into account the resources and labor involved each day in cleaning and cooking this catch.