Motion generation for legged mobile robots, which are characterized by an underactuated free-floating base, has become an important research topic in recent years. Although several research groups have addressed the problem of controlling the base in their own implementations, there is no work that completely describes the framework used to handle it, which makes it complicated for new researchers to find a proper solution. This paper aims at bridging this gap and presents a step-by-step guide to model the effect of the floating base on the kinematics of the robot, and to properly control it to achieve whole-body motion. The proposed framework is generic and can be applied to any legged underactuated robot such as a humanoid robot, a quadruped, an hexapod, amongst others. The results show an example of implementation using the model of a quadruped robot.