I mainly use my brushes for acrylics, so they aren't too "beat up". When I clean acrylic craft paint off my brushes, I use water.
Once the brush is in the water, gently push it against the bottom of the container and swipe back and forth. Make sure you use room temperature or cold water. Otherwise, the bristles of the brush can fall out.
When I use my brushes for nail polish, I use polish remover to clean them. Follow the same method as with the water. Take a cotton pad soaked in polish remover and swipe the brush back and forth on it until the colour comes off. I use non-acetone remover, which is not only easier on my brushes, but also on my nails.
I had the problem a couple of years ago where I dipped my brush in polish remover to clean it and then rubbed off the paint and the bristles came out! Since I've cleaned my brushes this way, I've had no mishaps. I hope this helps!