We have developed a model of the high-energy accretion region for magnetic cataclysmic variables and applied it to Extreme Ultraviolet Explorer observations of 10 AM Herculis type systems. The major features of the EUV light curves are well described by the model. The light curves exhibit a large variety of features such as eclipses of the accretion region by the secondary star and the accretion stream and broad dips caused by material very close to the accretion region. While all the observed features of the light curves are highly dependent on viewing geometry, none of the light curves are consistent with a flat, circular accretion spot whose light curve would vary solely from projection effects. The accretion region immediately above the white dwarf (WD) surface is a source of EUV radiation caused by either a vertical extent to the accretion spot or Compton scattering off of electrons in the accretion column or, very likely, both. Our model yields spot sizes averaging 0.06RWD, or f ~ 1 × 10-3 the WD surface area, and average spot heights of 0.023RWD. Spectra extracted during broad-dip phases are softer than spectra extracted during the out-of-dip phases. This spectral ratio measurement leads to the conclusion that Compton scattering, some absorption by a warm absorber, geometric effects, an asymmetric temperature structure in the accretion region, and an asymmetric density structure of the accretion column are all important components needed to fully explain the data. Spectra extracted at phases where the accretion spot is hidden behind the limb of the WD, but with the accretion column immediately above the spot still visible, show no evidence of emission features characteristic of a hot plasma.