First, soap and lukewarm water, scrub the stain. Lift up the stain by patting it dry with a clean rag. Or, use a carpet cleaner. Use vinegar in the rinse-water if your carpet wont stain from that - it will help neutralize the urine/ammonia/soap. Again, lift up using clean rags (or a carpet cleaner).

Bile soap or lemon soap can help on those hard-to-get-out stains. Ask people with young children where they get theirs (it is a fair bet they deal with poo and other stains on the regular).

Secondly, use enzyme-cleaner. Some carpet-cleaner-products claim to have those enzymes, but I have found products such as "urine off" are much much more effective. Remember to treat at least double the area, because urine will spread a lot and you need this product to cover at least the same area. This will take care of any lingering smells - even to the point where the dog wont notice the smell.

For about 10+ years I've been cleaning a dog-school where puppies may have accidents, using a black-light to make sure I've gotten it all (and a dog to double-check and supervise). If it glows in UVA-light, it needs more cleaning. If the dog says so, it needs more cleaning. Repeat procedure.

This works. Some nurses found it hysterically funny that our cleaning-routine meant our place was cleaner than a hospital room.