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Due to its salient features including real time pricing and distributed generation, the smart grid (SG) poses great challenges for energy management in the system. In this paper, we investigate optimal energy management for the SG, taking into consideration unpredictable load demands and distributed energy resources. Both delay intolerant (DI) and delay tolerant (DT) load demands are studied. We aim to optimally schedule the usage of all the energy resources in the system and minimize the long-term time averaged expected total cost of supporting all users' load demands. In particular, we first formulate an optimization problem, which turns out to be a time-coupling problem and prohibitively expensive to solve. Then, we reformulate the problem using Lyapunov optimization theory and develop a dynamic energy management scheme that can dynamically solve the problem in each time slot based on the current system state only. We are able to obtain both a lower and an upper bound on the optimal result of the original optimization problem. Furthermore, in the case of both DI and DT load demands, we show that DT load demands are guaranteed to be served within user-defined deadlines. Extensive simulations are conducted to validate the efficiency of the developed schemes.