In a new branch of quantum computing, information is encoded into coherent states, the primary carriers of optical communication. To exploit it, quantum bits of these coherent states are needed, but it is notoriously hard to make superpositions of such continuous-variable states. We have realized the complete engineering and characterization of a qubit of two optical continuous-variable states. Using squeezed vacuum as a resource and a special photon-subtraction technique, we could with high precision prepare an arbitrary superposition of squeezed vacuum and a squeezed single photon. This could lead the way to demonstrations of coherent state quantum computing.