The Extreme Ultraviolet Explorer (EUVE ) satellite was employed for 5.46 days beginning on 1999 February 9.03 UT to acquire phase-resolved EUV photometric and spectroscopic observations of the AM Her-type cataclysmic variable V834 Centauri. The resulting data are superior to those obtained by EUVE beginning on 1993 May 28.14 UT because the source was approximately three times brighter, the observation was four times longer and dithered, and ASCA observed the source simultaneously. Although we do not understand the EUV light curves in detail, they are explained qualitatively by a simple model of accretion from a ballistic stream along the field lines of a tilted ([β, ψ] ≈ [10 • , 40 • ]) magnetic dipole centered on the white dwarf. In 1993 when the EUV flux was lower, accretion was primarily along the ϕ ≈ ψ ≈ 40 • field line, whereas in 1999 when the EUV flux was higher, accretion took place over a broad range of azimuths extending from ϕ ≈ ψ ≈ 40 • to ϕ ≈ 76 • . These changes in the accretion geometry could be caused by an increase in the mass-accretion rate and/or the clumpiness of the flow. The 75-140Å EUVE spectra are well described by either a blackbody or a pure-H stellar atmosphere absorbed by a neutral hydrogen column density, but constraints on the size of the EUV emission region and its UV brightness favor the blackbody interpretation. The mean 1999 EUV spectrum is best fit by an absorbed blackbody with temperature kT ≈ 17.6 eV, hydrogen column density N H ≈ 7.4 × 10 19 cm −2 , fractional emitting area f ≈ 10 −3 , 70-140Å flux ≈ 3.0 × 10 −11 erg cm −2 s −1 , and luminosity L soft ≈ 7.2 × 10 32 (d/100 pc) 2 erg s −1 . The ratio of the EUV to X-ray luminosities is L soft /L hard ≈ 40, signaling that some mechanism other than irradiation (e.g., blob heating) dominates energy input into the accretion spot. The 1999 SW hardness ratio variation can be explained by minor variations in kT and/or N H , but instead of tracking the SW count rate variation, the hardness ratio variation was sinusoidal, with a minimum (maximum) when the accretion spot was on the near (far) side of the white dwarf, consistent with the trend expected for an atmosphere with an inverted temperature distribution.