Cleaning your brushes and sponges is important. If your brush is loaded with dark blue eyeshadow, and you want to use a delicate shade of pink, obviously that is not going to work. Here are the best ways I've found to clean your brushes.
You can use a "stippling sponge" to clean powders off of your brushes. This is very useful when you are putting on make up and suddenly need a clean brush. Just rub the brush against the sponge until the powder is gone from the brush. You can buy expensive "dry cleaning" tools, but they are basically just fancy versions of the stippling brush. These are easily available at most makeup stores for very little money, or you can order them from Amazon. This won't work for brushes that have cream products on them, obviously.
Using Commercial Cleaners
These work very well, given the right one. They work for creams or powders, and the brushes dry within a minute or two. The best commercial cleaner I have used is Parian Spirit. It works well and leaves a nice perfume on the brushes. The only problem is the price. The best price I have found is around $20 USD for 16 ozs. If you need to order it, you can find it here. This has free shipping, so it's a pretty good deal. If you have an Alcone in your town, you can get it a couple of bucks cheaper there.
The best way to use this stuff, especially for larger brushes, is to put some cleaner in a spray jar. Take a paper towel, and fold it into a 'C' so it has a few layers of thickness. Put that down on the table. Spritz the brush a couple of times with the Parian, and then brush the paper towel. Repeat the application and brushing until no color comes off when you brush the towel. Usually once or twice is enough.
I recommend spraying because if you put some cleaner in a glass or jar, and then dip the brush in it, the brush will soak up an incredible amount of cleaner. Once in a while, you can do this with the smaller brushes, to "deep clean" them. But do this with a large fluffy brush, and your $20 bottle of Parian will be gone in a day or two.
Using Isopropyl Alcohol
This also works. If you want to use 99% Isopropyl, which is hard to find but cleans the best, it is also expensive. It is a couple of bucks cheaper than the Parian. I suspect that the main ingredient in the Parian is Isopropyl alcohol, to tell you the truth.
You can use lower concentrations of Isopropyl, which are available in most drug stores for a fraction of the cost of Parian or 99% Isopropyl. These take longer to clean, but do work. One good note here is that if you are concerned about bacteria, the lower concentrations (which are diluted with water), are supposed to be better at killing bacteria than the pure stuff.
Use it in the same way as you would the Parian cleaner, with a spray bottle, occasionally cleaning the smaller brushes with a 'deep clean' bath.
It's also possible to use dishwashing soap, and this works very well. I have found "Dawn", the original version, to work the best. It works as well or better than any of the commercial brush shampoo's I have tried. This is probably the cheapest solution. There are two problems with this method. The first is simply the wait time for the brushes to dry. It takes several hours, or more if the brush is large. The second is the risk to the brush. You have to be careful not to get any water down into the ferrule (that's the metal part of the brush that attaches to the handle). Most of the glue used to attach these is water soluble, so if it gets wet, even a little, over time your brush will fall apart. It is not that easy to re-attach.
To use it, put some soap in the bottom of a dish or jar. Ideally one with a flat bottom. Use a very tiny amount of water, and swab the brush around in the soap, then in your hand. Rinse out the soap, and repeat until there is no color left in the brush. Make sure you get all the soap out of the brush!
Brush off the excess water on the paper towels, and if the brush is large, "shape" it gently with your hand so it will dry in the proper shape. Then lay it down flat on paper towels to dry. This is important. DO NOT LET YOUR BRUSHES DRY STANDING UP. When I was first learning makeup, I destroyed 12 brushes in about two weeks time by following some "expert" advice I found on the internet to let the brushes dry standing up. This just allows water to get down into the ferrule, and will eventually cause the brush to separate from the handle.
Cleaning your Beauty Blender
I'm not going to lie to you. Cleaning your Beauty Blender is a real pain. But at $20 - $30 a pop, what other choice do we have? And you really have to clean it each time you use it since the foundation and contouring colors left on it will seriously impact your look the next time you use it if not cleaned first.
I have tried several methods: Using the commercial "Beauty Blender" shampoo, using soap and oil in various combinations, and using Dawn (as described above for the brushes). I find the Dawn works as well or better than any other cleaner, so I recommend that. I don't find that adding oil helps. It doesn't hurt, but it doesn't seem to do much.
I recommend using quite a lot of Dawn, and a mostly dry Beauty Blender. Put the Dawn in a flat bowl, compress the Beauty Blender with your hands, and then try to get it to soak up as much of the Dawn as possible. You want to saturate the sponge.
Then rub the sponge gently between your hands for several minutes. You can start running water into it around this time. Then repeat this as much as you need to get the sponge squeaky clean. I find this takes me anywhere from 10-15 minutes. As I said, a real pain.
It's crucially important to get all the soap out of the sponge. Keep soaking up the water and squeezing it out until there is no soap foam left in it. Then place it somewhere where all the surfaces are exposed so it will dry quickly. The original container is good. Just set it on that, and when it dries, it will pop back inside.
This is a pain, but it is worth it. I have a Beauty Blender which is over a year old, but is still practically the same color and effectiveness as it was when I bought it. I know they recommend replacing the Blender every six months. Maybe if you are doing makeup with it 10 times a day, every day, that is necessary. But I haven't found it to be the case.
Clearly, using Parian or Isopropyl alcohol for brush cleaning wins in every way, except for price. It's both quicker and easier on the brushes than using soap. However, the soap way works well, and it is the one I use most often for my own brushes.
For the Beauty Blender, there isn't a great solution. It's just soap and elbow grease, then wait for it to dry.
I hope this was helpful. If you have suggestions or ideas, you can message me on Twitter I'm always interested in better ways to do things.