Broadcast data delivery is encountered in many applications where there is a need to disseminate information to a large user community in a wireless asymmetric communication environment. In this paper, we consider the problem of scheduling the data broadcast such that the access latency experienced by the users is low. In a push-based system, where the users cannot place requests directly to the server and the broadcast schedule should be determined based solely on the access probabilities, we formulate a deterministic dynamic optimization problem, the solution of which provides the optimal broadcast schedule. Properties of the optimal solution are obtained and then we propose a suboptimal dynamic policy which achieves mean access latency close to the lower bound. The policy has low complexity, it is adaptive to changing access statistics, and is easily generalizable to multiple broadcast channels. In a pull-based system where the users may place requests about information items directly to the server, the scheduling can be based on the number of pending requests for each item. Suboptimal policies with good performance are obtained in this case as well. Finally, it is demonstrated by a numerical study that as the request generation rate increases, the achievable performance of the pull- and push- based systems becomes almost identical.