This paper proposes an architecture for achieving telexistence and teleoperation of humanoid robots. The architecture combines several technological set-ups, methodologies, locomotion and manipulation algorithms in a novel manner, thus building upon and extending works available in literature. The approach allows a human operator to command and telexist with the robot. Therefore, in this work we treat aspects pertaining not only to the proposed architecture structure and implementation, but also the human operator experience in terms of ability to adapt to the robot and to the architecture. The proprioception aspects and embodiment of the robot are studied through specific experimental results, which are treated in a high-level manner. Application of the proposed architecture and experiments incorporating user training and experience are addressed using an illustrative bipedal humanoid robot, namely the iCub robot.