If the stain is new and still wet, a thorough cold water rinse can remove the bulk of the urine and mitigate or remove any odor before it sets in. The best method for removing dog urine odors from upholstery depends on timing.
The first step if the stain is new is to blot the area thoroughly with paper towels to remove as much of the urine as possible. Following with a thorough rinse of clean, cold water generally removes most if not all of the urine. The water can be removed either by blotting or with a wet vacuum. Steam cleaning or any method involving heat will serve to set the odor into the fabric rather than remove it.
Enzymatic cleaners work best with stains of biological origin. The cultures in an enzymatic cleaner consume the urine to remove all of it as a last step. If the stain is already dried, white vinegar can still work to remove the odor.
Because urine contains ammonia, the lingering scent may actually encourage the dog to urinate there again. It is important to clean the area thoroughly since the lingering odor of urine will encourage the dog to mark the area again.