Cell signaling can be thought of fundamentally as an information transmission problem in which chemical messengers relay information about the external environment to the decision centers within a cell. Due to the biochemical nature of cellular signal transduction networks, molecular noise will inevitably limit the fidelity of any messages received and processed by a cell's signal transduction networks, leaving it with an imperfect impression of its environment. Fortunately, Shannon's information theory provides a mathematical framework independent of network complexity that can quantify the amount of information that can be transmitted despite biochemical noise. In particular, the channel capacity can be used to measure the maximum number of stimuli a cell can distinguish based upon the noisy responses of its signaling systems. Here, we provide a primer for quantitative biologists that covers fundamental concepts of information theory, highlights several key considerations when experimentally measuring channel capacity, and describes successful examples of the application of information theoretic analysis to biological signaling.