One of the fundamental tenets of quantum mechanics is the existence of superposition states, or states whose properties simultaneously possess two or more distinct values. At present, there is growing interest in the criterion of 'big' superpositions and massively entangled states for use in applications such as a quantum computer. This article discusses the first steps toward this goal by demonstrating a fundamental two-bit quantum logic gate and a 'Schrodinger cat'-like state of motion with a single trapped 9Be+ ion. Both experiments allow sensitive measurements of decoherence mechanisms which will play an important role in the feasibility of quantum computation.