Food becomes the top priority for survival in a long-term survival situation, after the demands for shelter, water, and heat have been met. All methods for acquiring food are time-consuming processes, each with their own benefits and shortfalls. The key to developing your food supply is diversification of your collection methods. Trapping has an advantage because once you build and set the trap, you don't have to wait around until the animal comes.
Deadfall traps are tricky to set up, but can be an effective method to kill small game animals. (Finding an injured bear in your perfectly executed deadfall is no fun.) They operate on the simple principle: a heavy weight is supported by a baited trigger, balanced by connections. Once the trigger is activated, the weight falls onto the unsuspecting prey. The trap falls, the animal is dead, you hope. (See: injured bear, above.)
The figure-four deadfall trap is an effective method for killing small animals for food. The construction follows a shape of the number 4, hence the name. The trap requires three sticks, generally several feet long, and a heavy object, like a rock or log. Each stick will need to be notched so they can pivot upon each other. The weight will be balanced atop the diagonal stick, while it is notched into the horizontal stick. The total weight of the system is balanced among the three points, keeping the structure in place until an outside force acts upon the trigger. The short end of the horizontal stick will be the baited trigger. The animal takes the bait, and knocks the heavy object onto your target.
Whenever possible, place your trap on a hard surface, like a rock, so the heavy object will crush the animal. If it's placed on soft ground, it will drive it into the ground, merely injuring the animal. Also, the vertical stick should be on the ground, but not dug in, as to allow an easy fall.
As stated earlier, deadfalls are tricky to set up, but once they are established, can be scattered in an extensive area. Take caution while baiting the traps. First, they could just as easily fall on you. Second, bear in mind the bait. If the local animals aren't eating from the ordinary food sources, they won't eat from yours.
Finally, I recommend you check your traps on a frequent basis, and keep some weapon handy. If your trap only injures an animal, they're ready to fight. You should end their misery quickly, and appreciate their sacrifice for you.