  This paper provides a detailed description of the data reduction and analysis
procedures that have been employed in our previous studies of spatial
fluctuation of the cosmic infrared background (CIB) using deep Spitzer IRAC
observations. The self-calibration we apply removes a strong instrumental
signal from the fluctuations which would otherwise corrupt our results. The
procedures and results for masking bright sources, and modeling faint sources
down to levels set by the instrumental noise are presented. Various tests are
performed to demonstrate that the resulting power spectra of these fields are
not dominated by instrumental or procedural effects. These tests indicate that
the large scale (>~30') fluctuations that remain in the deepest fields are not
directly related to the galaxies that are bright enough to be individually
detected. We provide the parameterization of these power spectra in terms of
separate instrument noise, shot noise, and power law components. Our
measurements of spatial fluctuations of the CIB intensity indicate the mean
emission from the objects producing the fluctuations is quite low (>~1 nW m-2
sr-1 at 3-5 micron), and thus consistent with current gamma-ray absorption
constraints. The source of the fluctuations may be high-z Population III
objects, or a more local component of very low luminosity objects with
clustering properties that differ from the resolved galaxies. Finally, we
discuss the prospects of the upcoming space-based surveys to directly measure
the epochs inhabited by the populations producing these source-subtracted CIB
fluctuations, and to isolate the individual fluxes of these populations.
