For finding them, looking on the internet might work. Depending on where you are in the world, maybe you could google-up some reviews in English or other languages you speak. Also ask around. If you're staying at a hotel, ask the desk staff. They can probably point you toward a good salon in your price range. Also, if you have a specific city in mind, ask here in the forum for the country you're in. Someone here may have a good recommendation. You could also try googling something like "English-speaking hairstylist" + the name of the city you're in...

I have never had a haircut in a country where I didn't speak the language, but I did work in a few salons as an assistant and as a receptionist years ago, in high tourist areas. Tourists who could not communicate with their words would often use hand gestures and would usually end up going to the magazines looking for pictures of what they wanted. Many people, even those who could speak the local language, would come in with photos of the hairstyles they wanted.

So I would say go in with a picture, maybe learn some basic words like short or long, or whatever, and be prepared to do a few hand gestures. If the stylist is experienced, they will probably understand what you want pretty quickly, I imagine.