For a painter, this guidance is akin to Mom telling you to eat your vegetables , and every artist knows this is the right thing to do. Do I do it? Not as often or as thoroughly as I should. It's my dirty little secret. I do treat my sables a bit better, but my bristle brushes take some abuse. I am trying to do better, but even after all of these years, I'm not quite there yet. The proper approach to brush care is to give your brushes a good rinse in solvent (for oil painting brushes) followed by a wash from the ferrules down to the tip with a brush cleaner or dish soap, pushing the remaining paint out as you go. Once thoroughly rinsed, push the remaining water out and reshape with your fingers and just a dab of the brush soap, or just with water and leave to dry.
Don't leave your brushes head down in paint thinner (I used to do that). The bristles will lose their shape sooner and eventually the ferrule will loosen from the wood handle and fall off. Don't leave them head down in oil either (that's what I often do now- walnut oil- especially if I plan to return to the easel the very next day). Better but still not the best practice is to rinse out with oil and then paint thinner, and wipe clean with paper towels and reshape (this I do most often). When I do wash my brushes, I like Master's brush soap. It does a good job of getting off dried paint, which happens often enough with delinquents like me. Nevertheless, once the damage has been done, the shape of your brushes will never be the same. So save yourself a lot of time and money by doing it right the first time.
P.S. And while you're at it, would it kill you to clean your palette every once in a while?