There are all kinds of methods for cleaning a brush. The issue really comes down to just what is it that you are trying to remove from the brush. Hard water scale? Fats (soap scum)? Two different problems. Here are some simple solutions.

Hard-water scale: Borax (commercially available 20 Mule Team Borax will do the trick). One teaspoon per 8oz of water, soak for 15 minutes, rinse thoroughly.

Fats (soap scum): Shampoo (yep, the same stuff you use on your head). Use a small amount of shampoo (preferably one containing Sodium Laurel Sulfate), lather away for 30 seconds or so, rinse thoroughly. Some men like to give a second shampoo, to insure a good cleansing. There are even men who apply a conditioner. Of course, the easiest solution to this problem is to thoroughly rinse your brush after each use so scum does not build up.

All purpose: First, soak the brush with dishwashing liquid (like Dawn) for about 5 minutes, to rid the brush of soap scum. Then in a solution of 1 part vinegar, 4 parts water, and a dash of glycerin, soak the brush for about 10 minutes, to strip hard-water scale build up and to condition the hair.

Some gents are not practicing good brush hygiene. I soak my brush in 120F+ water everyday before using it. I rinse, rinse, rinse the brush after use ensuring all soap is removed. In the last 5 or 6, or is it 12 or 15 years, I have cleansed brushes with borax twice. I have cleansed each NEW brush with shampoo and lightly conditioned it with conditioner prior to its first use. I think I have also shampooed and conditioned a brush or two on one or two other occasions. I keep them clean and do not have especially hard water with which to deal. - Author wishes to remain anonymous (excerpt from an actual email received by QED)