Thousands of functional magnetic resonance imaging (fMRI) studies have provided important insight into the human brain. However, only a handful of these studies tested infants while they were awake, because of the significant and unique methodological challenges involved. We report our efforts to address these challenges, with the goal of creating methods for awake infant fMRI that can reveal the inner workings of the developing, preverbal mind. We use these methods to collect and analyze two fMRI datasets obtained from infants during cognitive tasks, released publicly with this paper. In these datasets, we explore and evaluate data quantity and quality, task-evoked activity, and preprocessing decisions. We disseminate these methods by sharing two software packages that integrate infant-friendly cognitive tasks and eye-gaze monitoring with fMRI acquisition and analysis. These resources make fMRI a feasible and accessible technique for cognitive neuroscience in awake and behaving human infants.