The Supernova/Acceleration Probe (SNAP) is a proposed space-based experiment designed to study the dark energy and alternative explanations of the acceleration of the Universe's expansion by performing a series of complementary systematics-controlled astrophysical measurements. We here describe a self-consistent reference mission design that can accomplish this goal with the two leading measurement approaches being the Type Ia supernova Hubble diagram and a wide-area weak gravitational lensing survey. This design has been optimized to first order and is now under study for further modification and optimization. A 2-m three-mirror anastigmat wide-field telescope feeds a focal plane consisting of a 0.7 square-degree imager tiled with equal areas of optical CCDs and near infrared sensors, and a high-efficiency low-resolution integral field spectrograph. The instrumentation suite provides simultaneous discovery and light-curve measurements of supernovae and then can target individual objects for detailed spectral characterization. The SNAP mission will discover thousands of Type Ia supernovae out to z = 3 and will obtain high-signal-to-noise calibrated light-curves and spectra for a subset of > 2000 supernovae at redshifts between z = 0.1 and 1.7 in a northern field and in a southern field. A wide-field survey covering one thousand square degrees in both northern and southern fields resolves {approx} 100 galaxies per square arcminute, or a total of more than 300 million galaxies. With the PSF stability afforded by a space observatory, SNAP will provide precise and accurate measurements of gravitational lensing. The high-quality data available in space, combined with the large sample of supernovae, will enable stringent control of systematic uncertainties. The resulting data set will be used to determine the energy density of dark energy and parameters that describe its dynamical behavior. The data also provide a direct test of theoretical models for the dark energy, including discrimination of vacuum energy due to the cosmological constant and various classes of dynamical scalar fields. If we assume we live in a cosmological-constant-dominated Universe, the matter density, dark energy density, and flatness of space can all be measured with SNAP supernova and weak-lensing measurements to a systematics-limited accuracy of 1%. For a flat universe, the density-to-pressure ratio of dark energy or equation of state w(z) can be similarly measured to 5% for the present value w{sub 0} and {approx} 0.1 for the time variation w' {triple_bond} dw/d ln a|{sub z=1}. For a fiducial SUGRA-inspired universe, w{sub 0} and w' can be measured to an even tighter uncertainty of 0.03 and 0.06 respectively. Note that no external priors are needed. As more accurate theoretical predictions for the small-scale weak-lensing shear develop, the conservative estimates adopted here for space-based systematics should improve, allowing even tighter constraints. While the survey strategy is tailored for supernova and weak gravitational lensing observations, the large survey area, depth, spatial resolution, time-sampling, and nine-band optical to NIR photometry will support additional independent and/or complementary dark-energy measurement approaches as well as a broad range of auxiliary science programs.