That said you can come across some primitive situations. You should carry tissues with you as free toilet paper is not the norm outside five star hotels. When you are on the road if you can ask your guide to keep a lookout for good toilets then they can usually find you a good option. Many public toilets have western style as well as squat style.
Chinese toilets are normally the squat style, which do take some getting used to but on the other hand you don't touch anything, so generally I don't mind them. Hotels all have western toilets now so you can rest assured in your own private room you will have a throne to relax on.
You will want to know how to recognize which toilet is for your sex and how to read the characters "public toilet". You don't have to be able to read Chinese - it is pattern recognition. Stare at the male and female a while, or copy them repeatedly on paper. Carry them with you and look at them while waiting in a line.
"Gong cuo" literally translates as "public toilet". You might see it on a sign post at an intersection or the side of a bathroom looking building. There are actually plenty of public toilets in Beijing if you keep your eyes open.
It also helps to be able to ask
Toilets in China vary greatly, which is probably why the government has started rating them with stars and handing out awards. I've never seen any awarded less than 3 stars - one and two star toilets don't seem to get labeled.