Two-state quantum systems may be used for encoding information in ways analogous to the bits of a conventional computer. Unlike discrete classical bits, however, quantum bits (qubits) may occupy superposition states in which they are simultaneously both 0 and 1. By manipulating such qubits it is possible to store and process information in new and powerful ways. Computation utilizing these superposition states would be extremely powerful, permitting efficient solution of some classically intractable problems such as factoring large numbers and simulating other quantum systems. I will describe how calcium ions, trapped in vacuum and probed with lasers, are one attractive candidate for processing quantum information. We load ions into surface electrode traps, a simple trap architecture in which all of the trap electrodes lie in a common plane. By applying static and time-varying potentials to the trap electrodes we are able to demonstrate exquisite control over the positions of individual ions and ion chains stored in the trap. A sequence of pulses from various lasers allows us to cool the ion motion and encode information which may later be read out by imaging ion fluorescence onto a camera. Individual encoding pulses may also be replaced with composite sequences to compensate for errors in pulse duration and intensity, an essential step in making computation fault tolerant.