To remove dog urine from carpet, mix one-part water with one-part vinegar, apply it to the urine stain, and scrub the solution into the area. Repeatedly blot the entire area with clean paper towels. Consider using a wet vac on the area and applying odor neutralizer for further cleanup.
A wet vac is a machine that shoots clean water down into the carpet and then sucks it back up. Wet vacs are available for rent at many hardware stores. Once the carpet is completely clean of dog urine, consider spraying odor neutralizer on the area so that the dog does not urinate there again. Many pet stores offer odor-neutralizing sprays.