Tangible Augmented Reality (AR) systems imbue physical objects with the ability to act and respond in new ways. In particular, physical objects and gestures made with them gain meaning that does not exist outside the tangible AR environment. The existence of this new set of possible actions and outcomes is not always apparent, making it necessary to learn new movements or gestures. Addressing this opportunity, we present visual hints, which are graphical representations in AR of potential actions and their consequences in the augmented physical world. Visual hints enable discovery, learning, and completion of gestures and manipulation in tangible AR. Here, we discuss our investigation of a variety of representations of visual hints and methods for activating them. We then describe a specific implementation that supports gestures developed for a tangible AR user interface to an electronic field guide for botanists, and present results from a pilot study.