Here's a link that tells you how, depending on the type of paint you use:
I wash mine with dish detergent and water in the palm of my hand until the water runs clean.. then taper the bristles and store upright.
You can soak in a diluted vinegar water solution.
I use hand pump soap or shampoo.
what medium do you use? Watercolor, acrylic, oil?
Hi Amy, not sure if you are using oil or acrylic, here is for oil, hope it helps you