Laboratory and computational experiments are often time and resource intensive, which motivates the fundamental question: how to optimally design an experimental campaign (e.g., sequence of experimental conditions) or an experimental apparatus (e.g., select sensors) to maximize the value of information gained under a constrained budget. In this brief tutorial, we share out recent experiences using data-driven Bayesian optimization, classical model-based experiment design, and hybrid approaches. We will summarize key benefits of each approach, offer recommendations how to choose the best method for a specific problem, and provide best practices.