You are right, how to remove cat urine from carpet is an old and common issue in cat households. The problem and solution are always two fold, first - stop the behavior and any ongoing inappropriate urination and second -get rid of the cat urine odor. To deal with the first thing, stopping the behavior, make sure you have good litter box care and understand the common reasons for inappropriate elimination. We have two good article to help you - the first is The Top 8 Reasons Why Your Kitty Won't Use the Litter Box and the helpful article is The Fine Art of Litter Box Care.
To deal with the second issue, that is how to remove cat urine odor from carpet - first - use white papertowels to soak up any wet urine. Keep blotting until you no longer can soak up any wetness. There are no good home remedies for how to remove cat urine from carpet. The most effective solution we have found is the use of commercial products. These products neutralize and break down the source of the urine odors. This is really the only way to eliminate the smell so your cat won't return to the area. Products include: Zero Odor, Urine-off, Nature's Miracle, SeaYu Petrotech Odor Eliminator, Anti Icky Poo (AIP), Odornil, Odorban, and Nilodor. Some products come with “money back guarantee”.
IMPORTANT: Follow instructions carefully on the labels of these products.