How is movement of individuals coordinated as a group? This is a fundamental question of social behaviour, encompassing phenomena such as bird flocking, fish schooling, and the innumerable activities in human groups that require people to synchronise their actions. We have developed an experimental paradigm, the HoneyComb computer-based multi-client game, to empirically investigate human movement coordination and leadership. Using economic games as a model, we set monetary incentives to motivate players on a virtual playfield to reach goals via players' movements. We asked whether (I) humans coordinate their movements when information is limited to an individual group member's observation of adjacent group member motion, (II) whether an informed group minority can lead an uninformed group majority to the minority's goal, and if so, (III) how this minority exerts its influence. We showed that in a human group--on the basis of movement alone--a minority can successfully lead a majority. Minorities lead successfully when (a) their members choose similar initial steps towards their goal field and (b) they are among the first in the whole group to make a move. Using our approach, we empirically demonstrate that the rules of swarming behaviour apply to humans. Even complex human behaviour, such as leadership and directed group movement, follow simple rules that are based on visual perception of local movement.