  We present the results of our analysis of cosmic-ray electrons using about 8
million electron candidates detected in the first 12 months on-orbit by the
Fermi Large Area Telescope. This work extends our previously-published
cosmic-ray electron spectrum down to 7 GeV, giving a spectral range of
approximately 2.5 decades up to 1 TeV. We describe in detail the analysis and
its validation using beam-test and on-orbit data. In addition, we describe the
spectrum measured via a subset of events selected for the best energy
resolution as a cross-check on the measurement using the full event sample. Our
electron spectrum can be described with a power law $\propto {\rm E}^{-3.08 \pm
0.05}$ with no prominent spectral features within systematic uncertainties.
Within the limits of our uncertainties, we can accommodate a slight spectral
hardening at around 100 GeV and a slight softening above 500 GeV.
