As a professional carpet cleaner in Tampa FL I deal with pet stains on a daily basis. This video shows how to make a pet stain carpet cleaner, but it could use some tweaking. There is nothing wrong with using Borax to remove stains and odors from carpet, however, I prefer baking soda instead. Baking soda and Borax have similar properties including the same pH. Baking soda seems to do a better job of eliminating odors and is slightly salty on its own, eliminating the need for salt in this pet stain carpet cleaner.
Mixing baking soda and vinegar with create a reaction that releases carbon dioxide and violent bubbling will occur. Anyone who has ever made a science project volcano has seen this reaction up close. So don't mix the baking soda with the vinegar. Instead, mix the 1/4 cup of vinegar with 3/4 cup of water as the base for your solution.
So the first step is to sprinkle the baking soda over the pet stains in the carpet and let it sit there for about 5 minutes. Then using a brush apply the mixture of vinegar and water. You could use a spray bottle to apply the water vinegar solution but the added agitation from the brush will better coat the carpet. If you don't have a brush or a spray bottle just pour the vinegar water solution onto the stain. Allow 15 minutes for the pet stain carpet cleaner to work on the odors and remove the stain.
Finally you can blot the whole thing up with a clean white towel. This will remove all the surface pet stain out of the carpet. If the stain has penetrated the carpet and has gotten into the pad underneath you will need to bring in a professional carpet cleaner who has experience with removing pet stains in carpets.