The goal of BridgeWars is to bring the points of the opponent team down to 0. You do this by standing in their scorearea, marked with particles. The more players standing in the scorearea, the faster the points go down. You can buy stuff using sandstone by clicking on the Shop signs. These are often located near spawn.
Bridge upwards at the start of the game to get a height advantage. Save some sandstone in the chest near spawn to buy stuff later. BridgeWars is all about rushing, so even if you know you're going to die, removing points is highest priority.