Information theory, though originally developed for communications engineering, provides mathematical tools with broad applications across science. These tools characterize the fundamental limits of data compression and transmission in the presence of noise. Here, we present a visual, intuition-driven guide to key concepts in information theory. We show how entropy, mutual information, and channel capacity follow from basic probability, and how they determine the shortest possible encoding of a data source and the maximum rate of reliable communication through a noisy channel. Our presentation assumes only a familiarity with basic probability theory.