First of all, in English we call someone who cuts men`s hair a barber, while we call someone who cuts women`s hair a hairstylist. I`ve noticed that in Japan there are many male hairstylist, while in America this job is done mostly by women.
There are different ways to talk about different types of haircuts. For example, right now I want my hair to be longer, so I only want the dead ends of my hair to be cut off. I could say to my hair stylist "I`m trying to grow my hair out, so I only want a trim." If you want more than a trim, which means only cutting off a centimeter or two, then you can tell a hairstylist to " take off ____centimeters". If you have have really long hair, and you want to get a lot of hair cut off then you can say you want to "chop it off".
As for communicating how long you want your hair to be, you can say that you want it to be "to my ears", "collar bone length", or "shoulder length". You can also say short, medium, or long if you don`t need to be specific.
If you want some of the top sections of your hair to be shorter than the rest, you can ask for "layers". If you want some of your hair to be cus so that it sweeps across your face you can ask for "bangs".
These days many people change the color of their hair, in English we call this dyeing your hair. For hair color we have 4 basic categories: brown, blonde, black, and red. You`ll often hear brown refered to as brunette. If you want streaks of another color in your hair, you can ask for "highlights".
There are so many ways to talk about hair, I couldn`t possibly list them all here, but I hope this blog gives you a couple new phrases you can use