  This is the first in a series of papers presenting methods and results from
the Young Solar Analogs Project, which began in 2007. This project monitors
both spectroscopically and photometrically a set of 31 young (300 - 1500 Myr)
solar-type stars with the goal of gaining insight into the space environment of
the Earth during the period when life first appeared. From our spectroscopic
observations we derive the Mount Wilson $S$ chromospheric activity index
($S_{\rm MW}$), and describe the method we use to transform our instrumental
indices to $S_{\rm MW}$ without the need for a color term. We introduce three
photospheric indices based on strong absorption features in the blue-violet
spectrum -- the G-band, the Ca I resonance line, and the Hydrogen-$\gamma$ line
-- with the expectation that these indices might prove to be useful in
detecting variations in the surface temperatures of active solar-type stars. We
also describe our photometric program, and in particular our "Superstar
technique" for differential photometry which, instead of relying on a handful
of comparison stars, uses the photon flux in the entire star field in the CCD
image to derive the program star magnitude. We present time series plots of our
spectroscopic data for all four indices, and carry out extensive statistical
tests on those time series demonstrating the reality of variations on
timescales of years in all four indices. We also statistically test for and
discover correlations and anti-correlations between the four indices. We
discuss the physical basis of those correlations. As it turns out, the
"photospheric" indices appear to be most strongly affected by continuum
emission. We thus anticipate that these indices may prove to be useful proxies
for monitoring continuum emission in the near ultraviolet.
