Invest in good brushes - good doesn't have to mean expensive. I've gotten some of my favorite brushes at the art supply store! When applying makeup, don't use anything that looks like a sponge. Use high-quality brushes made of animal hair (cruelty-free of course) for dry makeup, and taklon for any "wet" makeup. When I say dry, I'm referring to your eye shadow, powder, blush, eye brow powder, and so on. When I say wet, I'm referring to: lip color, liquid foundation, primer, and concealer.
Types of brushes and how to use them:
Eye shadow - You want a variety of sizes here, from about 1/2 inch wide and dense, to 1/8 of an inch and pretty short. I like the wider ones for applying the lighter shades over the entire lid, and the smaller ones for applying darker shades close to the lash line, and in the crease. A fluffy brush is great for blending.
Your eye shadow brushes should be made of real animal hairs, as the fibers pick up and hold the eye shadow, and then deposit and spread it over the eye lid much more effectively than synthetic fibers that don't have any texture to them.
Blush and powder - Again, animal hairs are best to pick up and deposit that color onto your skin. For blush, I like an angled brush, about an inch and a half wide at the top of the bristles. The angle is perfect for sweeping the blush in an upward motion along your cheekbone.
For powder and bronzer, I use my biggest brush, a big, fluffy thing that will cover the entire face. Or if used with a light hand, will just deposit powder or bronzer onto the broader planes of your face (cheeks, forehead, chin).
Secret Weapon - A fan brush is any makeup artist's secret weapon. It's like a miniature broom that sweeps away fallen eye shadow on the tops of the cheekbones after creating a smokey eye. It's also great for applying any highly-pigmented colors of blush with a really light hand. Because the fibers are spread apart, they deposit a very light amount of makeup, so you can control the amount much more easily.
The fan brush is also great for applying highlighter and/or bronzer if you just want a light amount to "kiss" your cheekbones, bridge of your nose, and forehead.
Taklon brushes - Because taklon is a synthetic fiber, it makes it great for applying liquid, gel, or cream-based makeup. I have a variety of sizes, just for applying liquid foundation. A smaller one (1/3 inch wide) is perfect for applying under-eye concealer and eye lid primer. And an even smaller one (1/4 inch), works well for lipstick, lip gloss, and lip stain.