What is the best solution to clean a female dog's private parts?

If you are cleaning it outside of the bath, I recommend using hypoallergenic baby wipes. It's easy and not messy and it does the job. For a good cleaning, a sensitive skin dog shampoo is best. Always water down your shampoo, 10 parts water and 1 part shampoo. Squirt your shampoo mix in the area and you can use a cloth instead of your hand if you would rather. The most important step is to rinse the area well after the shampoo washing. Residue can cause irritation.