This is one of my most useful recent purchases – a silicone makeup brush cleansing mat. It has suction cups on the reverse side for easier use.
I use cream eyeshadow and suck at applying it with my fingers, so I use an eyeshadow brush. This mat is the most thorough way I have found to clean them. I put shampoo or hand wash (though I should probably buy some proper brush cleansing solution) onto the pad, dilute it with a little water, and then move the brush around the different textures in a circular motion. It is horrifying how much comes out. After that I rinse the brush and then the pad.
I believe the different textures work for different types of brushes, but I only have eyeshadow brushes.
This pad came from H&M, but you can get them in most places that sell beauty accessories, and on Amazon.