An acoustic communication network is considered which consists of a number of bottom-mounted nodes operating in shallow water. The information gathered by the nodes' sensors has to be transmitted to the master node, and the goal of network design is to develop a communications method which provides a good trade-off between maximizing the information throughput and conserving the energy consumed by the battery-powered nodes. Towards this goal, a network protocol is proposed by which the nodes, upon initial deployment, establish a set of routes for communicating to the master node. The protocol is based on packet relaying, rather than direct access to the master node. It provides an autonomous network power-up from sleep, or energy-conserving mode, and enables the communication nodes, which initially had no inter-connections or knowledge of locations of other nodes, to become fully connected to the master node. Packet transmission proceeds via the established multi-hop connections, which may subsequently be adjusted according to a chosen dynamic routing algorithm.