The subject of nonmonotonic reasoning is reasoning with incomplete information. One of the main approaches is autoepistemic logic in which reasoning is based on introspection. This paper aims at providing a smooth introduction to this logic, stressing its motivation and basic concepts. The meaning (semantics) of autoepistemic logic is given in terms of so-called expansions which are usually defined as solutions of a fixed-point equation. The present paper shows a more understandable, operational method for determining expansions. By improving applicability of the basic concepts to concrete examples, we hope to make a contribution to a wider usage of autoepistemic logic in practical applications.