Some engines function as a sort of "white pages" directory. They collect E-Mail addresses from publicly-available sources (newsgroups, mailing lists, etc.) as well as from addresses that users submit to them. The engines list the addresses according to name, workplace, academic institution, etc.
When you want to find a person's E-Mail address, open one of these engines (Four11, The Internet White Pages, or LookUP), type in data on the person you're looking for, and search.