  In this thesis, I explore two topics in exoplanet science. The first is the
prevalence of Earth-size planets in the Milky Way Galaxy. To determine the
occurrence of planets having different sizes, orbital periods, and other
properties, I conducted a survey of extrasolar planets using data collected by
NASA's Kepler Space Telescope. This project involved writing new algorithms to
analyze Kepler data, finding planets, and conducting follow-up work using
ground-based telescopes. I found that most stars have at least one planet at or
within Earth's orbit and that 26% of Sun-like stars have an Earth-size planet
with an orbital period of 100 days or less.
  The second topic is the connection between the properties of planets and
their host stars. The precise characterization of exoplanet hosts helps to
bring planet properties like mass, size, and equilibrium temperature into
sharper focus and probes the physical processes that form planets. I studied
the abundance of carbon and oxygen in over 1000 nearby stars using optical
spectra taken by the California Planet Search. I found a large range in the
relative abundance of carbon and oxygen in this sample, including a handful of
carbon-rich stars. I also developed a new technique called SpecMatch for
extracting fundamental stellar parameters from optical spectra. SpecMatch is
particularly applicable to the relatively faint planet-hosting stars discovered
by Kepler.
