I’ll spare you the preaching of why it’s so important to clean you makeup tools regularly. By now, most of you know that they gather a lot of bacteria (including E. Coli) and that’s No Bueno when it comes to things that will have contact with your precious face. Here's an article from Good Housekeeping that lists all the “ew, yuck” stuff that can happen if you don’t clean your brushes.
To clean my make up brushes I wet them first then massage out all the residual product with a shampoo. I’ve just bought a cheap shampoo that I specifically use for my makeup brushes. Currently I'm using Schwarzkopf's Oil Nutritive Shampoo. Please note, I'm not saying you should use this product, this just works for me and I have no reaction to cleaning my brushes with it.
I use a dollop and then massage the bristles into the palm of my hand and rinse away with warm water until they’re no longer soapy.
Now for the beauty blenders, I love them but man are they annoying to clean. I’ve used shampoo and squeezed away. I also smushed them in a blend of olive oil and dish washer soap as instructed be Le Internet. This is actually pretty effective, but the problem with both these methods are that they require you to squeeze so much your hand starts cramping. So, I just toss them in the washing machine along with my clothes = no cramping. I did make the mistake of tossing two bright orange beauty blenders in with a dark wash and now they have a “nice” mud colour to them. Oops. Like my shampoo method for my make up brushes, I again am not saying that this is how you should clean your beauty blenders, this works for me and I've had no issues.