How much is a 1890's Smith and Wesson 38 pistol worth?

Your gun is likely a five shot top break chambered for .38 S&W (not the more modern .38 S&W Special). While the gun may function well, it is an antique which should not be routinely fired. It has primarily collector value which is based on the condition of the gun.

Have the gun appraised by a knowlegible gunsmith or collector.