Try using a wet vac to completely remove old urine from carpeting, then using a pet safe enzymatic cleaner to remove the remaining stain and odor. Pet safe commercial cleaners may used to remove stains as well.
Opt to clean pet stains in a three step process to reduce the chance of the animal coming back to the same spot later. The Humane Society suggests removing the urine with paper towels or a carpet extraction machine first, then removing any remaining odor with a cleaner that is specifically designed for pet stains. After removing the odor, the stain can be treated with oxygen bleach or carpet cleaning solutions.
Stain Solver recommends cleaning pet stains with a mixture of one tablespoon of powdered oxygen bleach dissolved in one quart of warm water. Apply the oxygen cleaner solution to the stain and wait for 5 to 10 minutes, then pat the area dry with a towel or clean with an extraction cleaner. Light-colored carpets can be cleaned using a solution of 50 percent water to 50 percent hydrogen peroxide using the same method as cleaning with oxygen cleaner. Commercial carpet cleaners and pet safe enzyme cleaners may be used according to the manufacturer's instructions on the label.
Neutralizing the odor left behind is the most important part of the cleaning process since the pet will continue to use the spot if traditional, non-enzyme based cleaners, such as chlorine bleach, are used.