The inherent limitations in scaling up ground infrastructure for future wireless networks, combined with decreasing operational costs of aerial and space networks, are driving considerable research interest in multisegment ground-air-space (GAS) networks. In GAS networks, where ground and aerial users share network resources, ubiquitous and accurate user localization becomes indispensable, not only as an end-user service but also as an enabler for location-aware communications. This breaks the convention of having localization as a byproduct in networks primarily designed for communications. To address these imperative localization needs, the design and utilization of ground, aerial, and space anchors require thorough investigation. In this tutorial, we provide an in-depth systemic analysis of the radio localization problem in GAS networks, considering ground and aerial users as targets to be localized. Starting from a survey of the most relevant works, we then define the key characteristics of anchors and targets in GAS networks. Subsequently, we detail localization fundamentals in GAS networks, considering 3D positions and orientations. Afterward, we thoroughly analyze radio localization systems in GAS networks, detailing the system model, design aspects, and considerations for each of the three GAS anchors. Preliminary results are presented to provide a quantifiable perspective on key design aspects in GAS-based localization scenarios. We then identify the vital roles 6G enablers are expected to play in radio localization in GAS networks.