From rain storms to ink jet printing, it is ubiquitous that a high-speed liquid droplet creates a splash when it impacts on a dry solid surface. Yet, the fluid mechanical mechanism causing this splash is unknown. About fifty years ago it was discovered that corona splashes are preceded by the ejection of a thin fluid sheet very near the vicinity of the contact point. Here we present a first-principles description of the mechanism for sheet formation, the initial stages of which occur before the droplet physically contacts the surface. We predict precisely when sheet formation occurs on a smooth surface as a function of experimental parameters, along with conditions on the roughness and other parameters for the validity of the predictions. The process of sheet formation provides a semi-quantitative framework for studying the subsequent events and the influence of liquid viscosity, gas pressure and surface roughness. The conclusions derived from this framework are in quantitative agreement with previous measurements of the splash threshold as a function of impact parameters (the size and velocity of the droplet) and in qualitative agreement with the dependence on physical properties (liquid viscosity, surface tension, ambient gas pressure, etc.) Our analysis predicts an as yet unobserved series of events within micrometres of the impact point and microseconds of the splash.