Glass formation and glassy dynamics are studied using a mobile cluster, static boundary model. For the two-dimensional Lennard-Jones glass, we examine the nature of the rearrangement processes that characterizes glassy dynamics, the correlation functions of the hexadic order parameter, the temperature dependence of the distribution of relaxation times, and the dependence of these properties both on the disorder within the static boundary and on the temperature. The mobile cluster passes from a low temperature disordered material to an intermediate temperature amorphized material to a high temperature liquid; during this thermal history, the distribution of relaxation times exhibits nonexponential behavior in the glassy region, and becomes Debye-like in the liquid phase. We see a chain of local structural rearrangements in a small cluster of eight particles representing characteristic elementary kinetic events in this very simple model of glass behavior. The possibility to interpret these events in terms of defect motion is discussed.