The twitch-up snare requires some construction, but it's an effective snare. It typically snaps the neck of your prey, eliminating the need for you to kill the animal once you've trapped it. Find a sapling that's growing along a well-used run and bend it across the trail. Use a piece of twine to hold the sapling over the trail and connect it to two sticks driven into the ground. The two sticks should be long enough to hold the sapling into position, but small enough to release when your prey enters the noose. Hang a noose from the sapling. When your prey walks through the noose, the pressure releases the sapling from the smaller sticks. As the sapling is released, it pulls back into an upright position, snapping the neck of your prey.
One big advantage that the twitch-up snare has over many other snares and traps is that the game, such as rabbits or groundhogs, are pulled into the air when they're captured. You generally want to stay away from the traps you've set so you don't deter your prey. But sometimes this also opens up the possibility that another predator will take your captured prey. If it's hanging in the air, that's less likely to happen.
Looking for something a little more simple? Try the deadfall.