The strong degeneracy of the 12C ignition layer on an accreting neutron star results in a hydrodynamic thermonuclear runaway, in which the nuclear heating time becomes shorter than the local dynamical time. We model the resulting combustion wave during these superbursts as an upward propagating detonation. We solve the reactive fluid flow and show that the detonation propagates through the deepest layers of fuel and drives a shock wave that steepens as it travels upward into lower density material. The shock is sufficiently strong upon reaching the freshly accreted H/He layer that it triggers unstable 4He burning if the superburst occurs during the latter half of the regular Type I bursting cycle; this is likely the origin of the bright Type I precursor bursts observed at the onset of superbursts. The cooling of the outermost shock-heated layers produces a bright, ~0.1s, flash that precedes the Type I burst by a few seconds; this may be the origin of the spike seen at the burst onset in 4U 1820-30 and 4U 1636-54, the only two bursts observed with RXTE at high time resolution. The dominant products of the 12C detonation are 28Si, 32S, and 36Ar. Gupta et al. showed that a crust composed of such intermediate mass elements has a larger heat flux than one composed of iron-peak elements and helps bring the superburst ignition depth into better agreement with values inferred from observations.