Frizzy hair occurs when the cuticle of the hair lifts up instead of laying flat. Dry hair is most often prone to frizziness because it absorbs moisture. This causes the cuticles to lift and fluff the hair out.
There are a few things that can be done to help avoid frizzy hair. Never brush dry, frizzy hair. Brushing hair while it's dry disturbs the cuticle, and it can also cause damage. For hair that is prone to frizziness, it's a good idea to comb through the hair while it's still wet. Frizzy hair can also be tamed by applying a small amount of conditioner to the tips of the hair while it's dry, which smooths down a rough cuticle.
Another way to help fight frizzy hair is to always use a protein-infused conditioner, which binds with the hair cuticle to fight frizziness and add shine.
Coloring the hair repeatedly can over-process the hair. This leaves the cuticle dry, damaged and prone to breaking. It's best to leave these products to a professional, or at least to avoid using these products very often. It's important to wait until the color grows out before attempting to color the hair again.