We analyze in detail how random fields are generated in a site-random uniaxial antiferromagnet when a uniform magnet field is applied. Explicit expressions are given for the mean-square random field. We also report on a systematic specific heat study of two three-dimensional Ising systems, pure FeCl2 and site-random Fe0.682Mg0.318Cl 2 (MG318), in constant applied fields. The contrasting behavior of the two provide a vivid demonstration of random-field effects. The unusual changes in the shape of the specific heat anomaly observed in MG318 are explained as crossover behavior and not a manifestation of new critical behavior. The crossover exponent φ associated with the random fields is determined from the shape of the magnetic phase boundary. We find φ=1.25±0.10, in excellent agreement with theoretical prediction.