You will need a snare made of aircraft cable. Snares are relatively inexpensive. Remember that most likely you will only get one catch out of a cable as they kink when an animal is caught.
Look for a place to set your snare. In a survival situation you are looking at animals such as rabbits, squirrels and muskrats.
If you are in an upland wooded area or field, look for paths in the thick grass or thickets. Make an educated guess on what type of animal is using the trail. This is important as it will dictate the size of you loop and height of the snare when set.
For example; a trail along a creek may be from raccoons, opossum and fox. The loop should be about six inches, use your fist on the ground with your thumb sticking up to determine the height of the bottom of the loop. In an aquatic area look for trails in the marsh or in the bottom of the pond. Most likely these are made by muskrats. Set your loop at 2-3 inches and an inch and a half of the ground. Most likely with muskrats your cable will be reusable as they are not large animals.
Center the snare in the middle of the trail.
Fasten it down to a solid anchor ( tree, fence, root). Remember the rule of thumb; you may be expecting a rabbit but prepare for an elephant.
The next day you may find your catch alive. Be prepared to dispatch the animal. In a survival situation you will need a club, it is a good idea to prepare one before you check your snare. A swift blow or two to the head is the most humane way of dispatching the animal without using a gun.