The dirthole is the most common method to catch coyotes. It simply is a hole in the dirt that mimics a fresh hole that a prey species has dug. There is a trap in front and one or more scents or baits in/near the hole to attract coyotes. It is effective as it exploits the coyotes natural curiosity to investigate the scents and digging.
It is simple to create. You dig a hole about 3-4 inches in diameter about 6-12 inches deep and at a 45 degree angle. In front of the hole you bed a leghold trap and cover it with dirt. Behind the hole, you use a backing which could be anything from a rock to a clump of grass. The scents go on the backing and bait goes in the hole. Scents generally used are red fox or coyote urine and bait is generally some type of meat. It is an effective way to catch coyotes in most circumstances.