  We present the power spectrum methodology used for the first-season COMAP
analysis, and assess the quality of the current data set. The main results are
derived through the Feed-feed Pseudo-Cross-Spectrum (FPXS) method, which is a
robust estimator with respect to both noise modeling errors and experimental
systematics. We use effective transfer functions to take into account the
effects of instrumental beam smoothing and various filter operations applied
during the low-level data processing. The power spectra estimated in this way
have allowed us to identify a systematic error associated with one of our two
scanning strategies, believed to be due to residual ground or atmospheric
contamination. We omit these data from our analysis and no longer use this
scanning technique for observations. We present the power spectra from our
first season of observing and demonstrate that the uncertainties are
integrating as expected for uncorrelated noise, with any residual systematics
suppressed to a level below the noise. Using the FPXS method, and combining
data on scales $k=0.051-0.62 \,\mathrm{Mpc}^{-1}$ we estimate $P_\mathrm{CO}(k)
= -2.7 \pm 1.7 \times 10^4\mu\textrm{K}^2\mathrm{Mpc}^3$, the first direct 3D
constraint on the clustering component of the CO(1-0) power spectrum in the
literature.
