Whipworms is the common name used for Trichuris Vulpis...a small, flat worm that infects the lower intestine of dogs. A dog generally gets this parasite by ingesting food or water (or feces) infected with the parasite.
The number one way of getting rid of this problem in your yard is by making sure that all fecal material is picked up. Dogs very often re-infect themselves by walking through feces that contains the eggs and then licking their feet later.
Unfortunately, whipworm eggs can survive in even a frozen environment for up to five years, so there is real no suitable method of removal of contamination completely. Replacing the soil or covering it with gravel or asphalt, as well as keeping your pet away from contaminated areas, will help prevent a whipworm problem.
You can also keep your dog on a monthly heartworm preventative (one that is effective against whipworms such as Heartguard) which will help keep his parasite load under control.
I hope this helps.