  The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has
measured the muon anomalous precession frequency $\omega_a$ to an uncertainty
of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data
collected in four storage ring configurations during its first physics run in
2018. When combined with a precision measurement of the magnetic field of the
experiment's muon storage ring, the precession frequency measurement determines
a muon magnetic anomaly of $a_{\mu}({\rm FNAL}) = 116\,592\,040(54) \times
10^{-11}$ (0.46 ppm). This article describes the multiple techniques employed
in the reconstruction, analysis and fitting of the data to measure the
precession frequency. It also presents the averaging of the results from the
eleven separate determinations of \omega_a, and the systematic uncertainties on
the result.
