The bright X-ray transient H1743-322 was observed daily by the Rossi X-ray Timing Explorer during most of its eight-month outburst in 2003. We present a detailed spectral analysis and a supporting timing analysis of all of these data, and we discuss the behavior and evolution of the source in terms of the three principal X-ray states defined by Remillard and McClintock (2006ARA&A..44...49R). These X-ray results are complemented by Very Large Array data obtained at six frequencies that provide quite complete coverage of the entire outburst cycle at 4.860GHz and 8.460GHz. We also present photometric data and finding charts for the optical counterpart in both outburst and quiescence.