A finite difference technique is presented for solving the equations of motion for an arbitrarily compressible fluid. The technique, which includes the Implicit Continuous-fluid Eulerian (ICE) method as an optional feature, is simplified to facilitate its use by persons with little or no experience in numerical fluid dynamics. This report describes the basic algorithm in detail, discusses some accuracy and stability considerations, includes a flow chart and a FORTRAN listing, and describes three test problems in detail.