According to Frugal Living Cleaning Pet Stains and Odors —

To get rid of dog or cat urine odors…
Soak up as much of the pet urine as you can using towels applying pressure from your weight. Sprinkle baking soda over area and leave overnight. Vacuum.

After baking soda, the article says to mix 2 c. white vinegar with 1 gal. water and use it to wash area. The vinegar smell will go away as it evaporates.

(Baking soda neutralizes acid odors while vinegar neutralizes alkaline odors. Almost any odor problem can be solved by one or both of these. Since pet urine is usually both acidic and alkaline, the above solution should prove quite effective in eliminating the odor.)

I tried the basic idea above. I had a tough spot on the carpet that just would not come clean after trying several off the shelf carpet cleaning solutions. The worst part was the odor (one of the dogs had an accident)…it was driving me nuts! I decided to try putting baking soda on the area and dampening it (not soaking) with hot water. I gently scrubbed it and pressed towels on it to try to lift the moisture.

After letting it set all night, came back the next morning and vacuumed. The odor was much less, but still there. Decided to try adding some white vinegar to the mix. Made up a solution of one part white vinegar to one and half parts hot water and applied it to the area. Did the gentle scrubbing and blotting action again. The stain and odor are now gone! (And, the “old” carpet looks SO clean!) No more RESOLVE® carpet cleaner for me.

See article for other ideas.

Nature’s Miracle® Stain & Odor Remover, an enzymatic cleaner, is recommended on many sites as being effective in removing pet stains (urine, vomit, blood, feces) and the offensive odors that sometimes come along with them. (They do offer a 100% money-back satisfaction guarantee, so really nothing to lose by trying.) There are other similar enzyme solutions available in stores.