  Very-high-energy (VHE, E \gtrsim 100 GeV) gamma rays emitted by extragalactic
sources, such as blazars, initiate electromagnetic cascades in the
intergalactic medium. The cascade photons arrive at the earth with angular and
temporal distributions correlated with the extragalactic magnetic field (EGMF).
We have developed a new semi-analytical model of the cascade properties which
is more accurate than previous analytic approaches and faster than full Monte
Carlo simulations. Within its range of applicability, our model can quickly
generate cascade spectra for a variety of source emission models, EGMF
strengths, and assumptions about the source livetime. In this Letter, we
describe the properties of the model and demonstrate its utility by exploring
the gamma-ray emission from the blazar RGB J0710+591. In particular, we
predict, under various scenarios, the VHE and high-energy (HE, 100 MeV \lesssim
E \lesssim 300 GeV) fluxes detectable with the VERITAS and Fermi Large Area
Telescope (LAT) observatories. We then develop a systematic framework for
comparing the predictions to published results, obtaining constraints on the
EGMF strength. At a confidence level of 95%, we find the lower limit on the
EGMF strength to be ~ 2 \times 10^{-16} Gauss if no limit is placed on the
livetime of the source or ~ 3 \times 10^{-18} Gauss if the source livetime is
limited to the past ~ 3 years during which Fermi observations have taken place.
