Ultrafast electron diffraction (UED) is developed, in this and the accompanying paper, as a method for studying gas-phase molecular structure and dynamics on the picosecond (ps) to femtosecond (fs) time scale. Building on our earlier reports (henceforth referred to as 1-3), we discuss theoretical and experimental considerations for the approach. Specifically we show that the use of rotational and vibrational coherences can add a new dimension to structural determination of gas-phase species. In addition to the internuclear separations of the molecular sample, the spatial alignment reflected in the scattering pattern contains bond angles and rotational constants for both excited-state and ground-state species. Vibrational coherence effects are also observable, and the motion of the wave packet is revealed by the change of the diffraction pattern with time, thus yielding the molecular dynamics. UED provides the temporal evolution of the reaction coordinate directly and is well-suited for studies of global structure changes on this time scale. Paper 5 details our experimental studies with UED and the current time resolution of the apparatus.