We present ways in which pulse sequences and polarizations can be used to extract structural information from one- and two-dimensional vibrational sum frequency generation (2D SFG) spectra. We derive analytic expressions for the polarization dependence of systems containing coupled vibrational modes, and we present simulated spectra to identify the features of different molecular geometries. We discuss several useful polarization combinations for suppressing strong diagonal peaks and emphasizing weaker cross-peaks. We investigate unique capabilities of 2D SFG spectra for obtaining structural information about SFG-inactive modes and for identifying coupled achiral chromophores. This work builds on techniques that have been developed for extracting structural information from 2D IR spectra. This paper discusses how to utilize these concepts in 2D SFG experiments to probe multioscillator systems at interfaces. The sample code for calculating polarization dependence of 1D and 2D SFG spectra is provided in the Supporting Information.