I was giving a talk earlier this evening to a WI (Women's Institute) group on the history of dictionaries and I was completely stumped by a question from a woman in the audience. She asked me if there were Chinese dictionaries and how they were organised. I am ashamed to say I didn't know, so I have just looked it up.
The Wikipedia page on the subject is complicated. From what I can see there are two popular ways of arranging a Chinese dictionary - by pronunciation and by so-called radicals, which are recurring parts of Chinese characters. The entries in dictionaries that are arranged by pronunciation are listed alphabetically by Pinyin spelling (ie romanised Chinese). In dictionaries organised by radicals, there is a core of 214 standard radicals to which sections of the dictionary are devoted. If you need to look up a character you first identify the radical and find that section of the dictionary. Then you count the remaining strokes in the character and the entries will be arranged by number of strokes added to that particular radical. You can look inside this OUP dictionary and see the list of radicals (not the full 214, as this is a dictionary for learners) and other pages.
This, in a very oversimplified nutshell, is how Chinese dictionaries are arranged. There is more information on this Wikipedia page devoted to section headers in a Chinese dictionary. Section header is another term for radical. All of these pages are pretty difficult to understand if you don't know any Chinese, which is my problem.