The essential point about web directories is that they are compiled by human beings. In the early days of the web, when Yahoo was young, they were the way we found things. But the number of pages they can manage is tiny in comparison with those found by computer-compiled search engines. That is not necessarily a bad thing, but these days directories try to have the best of both worlds by including computer-compiled listings as well.
Using a web directory
Directories are arranged using what is known as the "drill-down" system. On the opening page is a list of major subject headings. Go to one of these and you will find a list of narrower subjects, and so on, until you reach the individual pages. Do not be surprised if you find only a handful connected with your search: they may be good resources. You will find a search box on the opening page of the directory, and you can use that method if you prefer.
The big directories
The Open Directory Project is compiled by volunteers, but is American in outlook and owned by Netscape. Google also offers Google Directory, which shares the main site's clean look: selection and annotation is by the Open Directory's volunteers, but Google claims to enhance this with its own technology. Note that it has 1.5million pages: the main Google search engine indexes nearly 10 times as many.
About.com (and About.com UK) styles itself "the human internet". Its editors are named and pictured, and listings are accompanied by annotations. It's a bit like reading a magazine, with a contents page and features.
More authoritative altogether is The Librarians' Index To The Internet, a directory of web resources hand-edited by public librarians in the US. It has some 20,000 entries, all examined by human beings and claimed to be "websites you can trust". InfoMine is a directory of scholarly resources put together by academic librarians. These are not sites that you will use every day, but they do have their uses.