Microorganisms are the most abundant, diverse and functionally important organisms on Earth. Over the past decade, microbial ecologists have produced the largest ever community datasets. However, these data are rarely used to uncover law-like patterns of commonness and rarity, test theories of biodiversity, or explore unifying explanations for the structure of microbial communities. Using a global scale compilation of >20,000 samples from environmental, engineered and host-related ecosystems, we test the power of competing theories to predict distributions of microbial abundance and diversity-abundance scaling laws. We show that these patterns are best explained by the synergistic interaction of stochastic processes that are captured by lognormal dynamics. We demonstrate that lognormal dynamics have predictive power across scales of abundance, a criterion that is essential to biodiversity theory. By understanding the multiplicative and stochastic nature of ecological processes, scientists can better understand the structure and dynamics of Earth's largest and most diverse ecological systems.