Typically, the problems to be solved are of the sort that would normally be tackled by a human "expert" - a medical or other professional, in most cases. Real experts in the problem domain (which will typically be very narrow, for instance "diagnosing skin diseases in human teenagers") are asked to provide "rules of thumb" on how they evaluate the problems, either explicitly with the aid of experienced system developers, or sometimes implicitly, by getting such experts to evaluate test cases and using computer programs to examine the test data and (in a strictly limited manner) derive rules from that.
Simple systems use simple true/false logic to evaluate data, but more sophisticated systems are capable of performing at least some evaluation taking into account real-world uncertainties, using such methods as [fuzzy logic]?. Such sophistication is difficult to develop and still highly imperfect.
While expert systems have distinguished themselves in AI research in finding practical application, their application has been limited. Expert systems are notoriously narrow in their domain of knowledge - as an amusing example, a researcher used the "skin disease" expert system to diagnose his rustbucket car as likely to have developed measles, and thus prone to making errors that humans would easily spot. Additionally, once some of the mystique had worn off, most programmers realized that simple expert systems were essentially just slightly more elaborate versions of the decision logic they had already been using. Therefore, some of the techniques of expert systems can now be found in most complex programs without any fuss about them.
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