Painters will probably fuss about the "best way" to clean brushes as long as there are painters and brushes. What works "best" for one person might not suit another.

The most important thing about cleaning a brush is to eliminate the build-up of paint residues near the ferrule, at the "heel" of the brush!
The best way to do this is to grasp the tip of the brush hairs in one hand, and flex the hair-shafts by gently rotating the handle, when the brush is well-lathered with soap .

Here are some points you may find useful, or take issue with:

-As J.F. Carlson said, kerosene is the best solvent for washing brushes. Like baby oil (aka mineral oil or petroleum jelly - Vaseline) it has lubricating properties. It is the most penetrating of solvents commonly used for cleaning up because its wicking action is the highest. It readily "cuts" the oils and resins commonly used in oil painting, and it's relatively safer compared to other volatile solvents because of its low vapor pressure.

-Turpentine is NOT a good solvent for washing brushes, and eliminating all volatile solvents (whether you can smell them or not) in group sessions is a good idea. Using oils to clean brushes is a good solution in the classroom, so long as the brushes get a proper thorough cleaning after the session.

-Hog bristles are hollow. Soaking in oils renders them heavy, or "flabby" in action because the hair shafts fill with oil when they're soaked in it. The resulting action may or may not be something individual painters notice, or find offensive.

-Different cleaners for different hairs. "Fatted" soaps are best for hog bristles, (Ivory and a few of the brush soaps marketed for the purpose) but they leave sables matted and heavy. Lighter Castile soaps are better for sables used in oil paint. Detergents are anathema to the care of natural hairs, but work great on synthetics.

- "Hot" solvents such as lacquer thinner, xylene, acetone, citrus extract solvents and all paint removers are very damaging to natural hairs, and will embrittle them if used regularly. The first thing to break off are the "flags".

-Using a good quality pasty hair conditioner, any of the kinds that promise "beautiful, lustrous hair" is a good idea. The consistency of the conditioner enables re-shaping the brush after washing, which can eliminate "wave" and splayed hairs upon drying. I've noted definite improvement in my hog bristles since I began using it.

Lastly, the cleaning and care of brushes used in commercial paints, enamels and lacquers in the sign shop has little to do with caring for brushes used for "fine art" oil painting. The brushes are different, the materials are different, the uses are different, and expectations for longevity of the brushes are different.

I use the Dove shampoo/conditioner combo. It works great.