The majority of pet urine problems I deal with as a carpet and rug cleaner in Tampa FL are cat related. I found this video on how to clean cat urine stains and it has some sound advice. I would add that you want to try and get to a cat urine stain as soon as possible. The speed in which you soak up the urine will help determine how successful you are at removing the urine stain.
If you have a cat its a good idea to keep a enzymatic urine cleaner in the house. Accidents do happen. The best way to clean cat urine stains is to remove and spray nozzles on your urine cleaner an just pour it directly on the spot to adequately soak the area. Make sure the urine cleaner contacts all the urine. so it can break down the urine crystals and eliminate the odor.
If the urine spot is already dry your enzymatic cleaner can improve the situation but it will likely take several applications before it's completely neutralized. let it dry our completely between cleaning attempts to insure the enzymes have had time to do their job. If you are unable to clean out the cat urine stains it might be time to call in a professional carpet or rug cleaner.