How do search engines rank the information they give users?

After a search engine has searched for a query term entered by a user, it gives the user a list of links to web sites they believe contain the relevant information the user is looking for. Search engines rank the most relevant information at the top of the list, but the way that search engines determine which information is the most relevant differs in all search engines. Search engines do not all work the same, therefore if you search for the same term on three search engines, you will most likely not get the same documents.

In the article The Searching Quagmire by Susan Feldman and Elizabeth Liddy, they explain a number of ways that pages are ranked. Search engines can rank pages by query term frequency, location of terms, source of information, date of publication, length of document, number of matched query terms in the title of lead paragraph, popularity of site, or whether or not the site has paid for its ranking.

How do search engines decide what information is most relevant for their users? à