Traditionally, Chinese people read from right to left, and top to bottom. But with the arrival of European influence, the Chinese changed to reading from left to right, and top to bottom.
I took these photos on 01 July 2013 in the Forbidden City. Both of them say the same thing in Chinese. The one on the right says 皇家電話局 and the the one on the left says 局話電家皇. The one on the right is simplified as 皇家局电话. The more traditional way, right to left, is 局話電家皇, and the newer and more modern way is 皇家電話局.
It can sometimes be vital to know whether to read from right to left or left to right in Chinese. Often on very formal things, like business names, they might write the name right to left. It is very common in my experience to see signs written from right to left in Hong Kong, Taiwan, and Macau.
In Mainland China, I would say the vast majority of the time, probably 99% or more of the time, things are written from left to right, but once in a while you may run into some signs which need to be read from right to left.
Have you ever experienced confusion as to whether to read Chinese from left to right or right to left? Let’s discuss it in the comments below.