This is how I set up for cleaning my brushes. I use three glasses(sometimes four), a jar with dirty brushes and a clean towel. I roll the towel over one or twice so the brushes can lay on a slant. I recommend doing a wash at least once a week for all your brushes. I use a daily brush cleaner on my foundation, concealer, and all brushes used in a gel daily, but do a full shampoo to all brushes weekly. BTW, I am going to do an illustration (art major here) for this tutorial eventually, but for now here is the tutorial with photos.

I put alcohol in one glass, shampoo and water in another & then dishwashing liquid and water in the third. I also use a forth cup with alcohol that I dip the brushes in after rinsing for the brushes in my kit, but you don't need to do this. Alcohol for the stubborn lipstick, foundation, concealer. Shampoo for natural brushes. Dishwashing liquid for synthetic brushes. Add water to the shampoo and dishwashing liquid and stir.

Synthetic Brushes

Here is dirty a synthetic brush

Dip the brush into the dishwashing liquid/water mixture, make sure to dip just the bristles in, you don't want water to get into the ferrule (the metal part).

Swirl/brush the brush in your palm. Basically pretend you're painting your hand with soap. Never push the brush directing into your palm, you don't wanna push the bristles out, so the "brushing" motion is ideal.

Rinse in cold water and point the brush downwards. You want to use cold water so as to not melt the glue in the ferrule which will lead to shedding. You also want to point it downwards so as to not get any water dripping upwards into the ferrule, since that will also lead to shedding. (Repeat washing and rinsing as needed.)

Gently reshape the brush.

Place the brush on the towel with the handle on the rolled end. I know you'll see a lot of people doing elaborate setups to hang their brushes, and in my opinion this is just silly & too much work. I am not only an MUA but also a formally trained painter and I have watercolor brushes which are way more spendy than my makeup brush and I still use the same techniques to wash and dry them. I've never had trouble with water in the ferrule when laying brushes flat. TL:DR Laying your brushes down is enough, just don't go setting them upright in a jar or something.

Natural Brushes

Follow the same steps as above for your synthetic brushes, but use the shampoo/water mixture instead. Swirl in shampoo solution. Brush/swirl against palm. Rinse. (Repeat washing and rinsing as needed.) Reshape. Place on towel until dry.

Synthetic Brushes with Suborn Product

"Brush" the brush against the side of the cup and/or swirl it in the alcohol. The alcohol will help break down products that can get really stuck in synthetic brushes. I do this for my foundation and concealer brushes.